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CHARTOGRAPHY 

IN TEN LESSONS 



BYFRANKJ.WARNE 




TABLE OF CONTENTS 
PREFACE 
INTRODUCTION / 



PUBLISHED BY 

FRANKJ.WARNE 

SOUTHERN BUILDING 
WASHINGTON. D.C. 




/) 



CHARTOGRAPHY 

IN TEN LESSONS 



BY 

FRANK J. WARNE 

AUTHOR OF 

warne's book of charts 

warne's elementary course in 

chartography, etc. 



ILLUSTRATIONS BY H. F. CHURCH 



Published by 

FRANK J. WARNE, 

SOUTHERN BUILDING 

WASHINGTON, D. C. 



tbjfiM, 






Copyright, 1919, By F. J. WARNE 



(Authorship also protected in Great Britain and 
her Colonies, including Canada) 



NOV -7 I9J 



)Ci.A5364?3 U 



Recorded 



TABLE OF CONTENTS 

Page 

Preface • . vii 

Introduction IX 

Lesson I 

Building the Chart 

Value of Table of Contents 1 

Statistics and Chartography 3 

Definition of a Chart 3 

The Statistics 4 

Horizontal Lines 5 

Vertical Lines 6 

A Choice of Methods 8 

The Use of Pencil Dots 10 

The Framework. . 10 

\ Lesson II 

The Scales 

Statistical Variables 13 

The Independent Variable 13 

The Dependent Variable 14 

The Horizontal Scale 15 

Determining the Vertical Scale 15 

The Scale Lines 16 

Reading the Scales 17 

Plotting the Statistics 19 

The Use of Gradicules 20 

iii 



iv Chartography in Ten Lessons 

Lesson III 

The Curve Chart 

Page 

Making the Curve Heavier 25 

The Horizontal Scale Unit 26 

Squares Should be Equal 27 

Effects of Different Scale Units 28 

Dropping the Zero Line 30 

Indicating the Absence of the Zero Line 31 

Divisors for the Vertical Scale 33 

Lesson IV 

Features of a Complete Chart 

The Statistical Table 37 

Table Should Appear on Chart 39 

The Make-Up of the Table 40 

Spacing the Columns 41 

The Form of the Table 42 

Duplicating the Scale Units 44 

The Place for the Horizontal Scale 44 

Word Designation of the Scale 46 

The Title 47 

The Foot-Notes 48 

The Neat Lines 49 

Lesson V 

The Bar Chart 

Making Bars from a Curve 53 

Making a Curve from Bars 55 

Advantages of the Horizontal Bar 56 

Reversing the Scales 57 

Width of the Bar 59 



Table of Contents v 

Page 

Separation of the Bars 60 

Location of the Table 61 

The Bar and the Curve 62 

Lesson VI 

The Tools of the Chartographer 

Cross Section Paper . . 65 

The Lead Pencil 69 

The Kind of Ink 70 

The Ruling Pen 71 

Correct Position for Holding Pen 71 

Pen Points 73. 

The Drawing Board 74 

The T-Square 75 

The Triangle 75 

The Engineer's Scale 77 

The Dividers 78 

The Essential Tools 79 

Lesson VII 

Accuracy in Chartography 

The Use of the Typewriter 81 

Drawing Letters for the Title 83 

Exaggerating the Curve 86 

Effects of Exaggerating the Curve 88 

Advantages of Extra Squares 91 

Lesson VIII 

Curve and Bar Designations 

Disadvantages of the Unbroken Curve 93 

Curve Designations 95 



vi Chartogkaphy in Ten Lessons 

Page 

Word Designations of Curves 98 

The Peak-Top Curve 99 

Determining the Scale Spacing 101 

Utility of the Curve Chart 102 

Chartography Based on Comparisons 103 

Bar Designations 105 

Interpreting the Bar . . . 108 

Some Characteristics of a Good Bar Chart .... 109 

Word Designation of Scale Units Ill 

Lesson IX 
Value of Statistics to Chartography 

The Statistical Table 114 

Aids in Reading the Table 116 

The Substitution of Ciphers 119 

The Table of Ratios 1&0 

Building up a Table 12l 

The Percentage Increase and Decrease 1^3 

The Zero Line 1#6 

The Arithmetic Average 1^9 

The Misuse of the Average 13 1 

Statistical Class Limits 13<£ 

Lesson X 
Primary Principles of Chartography 

Planning the Chart 137 

Importance of the Right Method . 139 

Essentials of Good Chart Making 140 

Planning the Size of the Chart .141 

Planning a Reduction in Size . 143 

The Reducing Glass 147 

The French Curves 149 

Checking up the Completed Chart 151 



PREFACE 

No attempt is made in these ten Lessons to 
cover the entire field of chartography. To do so 
adequately would require several large volumes. 
All that these Lessons aim to do is to familiarize 
the student with the primary or elementary prin- 
ciples. These underlie chart plotting and con- 
struction as applied to the curve and bar charts. 
These principles are applicable to all kinds of 
charts, variations being explained by the differ- 
ences in the circumstances surrounding the special 
problems. 

These Lessons are the by-product of an experi- 
ence covering a period of ten years during which 
time the author has been engaged professionally in 
the application of the principles of chartography 
to the working out of practical problems of the 
work-a-day world. In the presentation by means 
of diagrams or charts of innumerable statistical 
problems the author has been able to put the art 
of chartography to a severe test before such 
authoritative tribunals as the Interstate Com- 
merce Commission, various state public utilities 
and railroad commissions, boards of arbitration 
appointed by the President of the United States 
for the peaceable settlement of labor contro- 



viii Chartography in Ten Lessons 

versies and various committees of Congress. In 
this professional work he has been called upon 
to till entirely new fields, for there were few 
authoritative guides to follow, and in conse- 
quence he has been compelled to pioneer his 
way amid innumerable uncharted difficulties. 
Such an experience should contain lessons of 
value to others engaged an\d about to engage in 
the making of charts. In presenting this formu- 
lation of the principles of chartography the 
author begs leave to express the hope that these 
Lessons may serve the beginner in chartography 
as a safe guide over the innumerable pitfalls that 
inevitably must be encountered unless he is 
warned to guard himself against them. 

An endeavor has been made to bring these 
Lessons within a reasonable price to the student. 
The cost of production of "Warne's Elementary 
Course in Chartography," which was published 
two years ago and the price of which was fifty 
dollars for the twenty Lessons (including 
"Warne's Book of Charts"), was such as to pro- 
hibit a lower price, and in consequence it could not 
be made to serve the class of students the author 
desired most to reach. Parts of that Course have 
been completely revised in these Lessons. 



INTRODUCTION 

The Value of Chartography 

{Revised from "Warne's Elementary Course in 
Chartography" and "Warne's Booh of Charts."") 

To the average citizen statistics are as incom- 
prehensible as a Chinese puzzle. To him they 
are a mental " Mystic Moorish Maze." He 
looks upon columns of figures with suspicion 
because he cannot understand them. Perhaps he 
has so often been misled by the wrong use of 
^statistics or by the use of incorrect statistics 
that he has become sceptical of them as repre- 
senting reliable evidence as to facts and, like an 
automaton, he mechanically repeats "while 
figures may not lie, all liars, figure," or the 
equally common libel, "there are three kinds of 
lies — lies, damn lies and statistics." 

And yet statistics are an infallible indicator of 
economic conditions — they measure the heart- 
throbs of a nation's or of an industry's life- 
blood. They register the conditions of any given 
static situation; they point the direction of a 
trend or tendency with the accuracy of the ther- 
mometer in measuring the temperature. 

Every business, whether organized on a large 
or a small scale needs statistics — in fact, statistics 



x Chartography in Ten Lessons 

are vital to its successful existence. Without 
them the executives cannot know the status or 
tendency of the economic factors which control 
their affairs. This practical value of statistics 
in every-day business life is coming to be more 
and more correctly appraised at its true worth. 
The Railway Age of February 23, 1917, says: 

An officer of a western road recently made 
the statement that each department of a large 
railroad system should have on its staff a thor- 
oughly competent man whose duty it should be 
to analyze statistics. The assertion was not 
made without deliberation, and it might be perti- 
nent to ask whether we are getting the most out 
of the statistical department. The amounts 
which are spent by American railroads in com- 
piling statistics bearing on the functions of the 
various departments are extremely large, and no 
one who knows the importance of the compara- 
tive figures to the officers will question the wisdom 
of the expenditure. Some of the statistical data 
which the railroads compile is readily analyzed, 
and the important figures, such as average tons 
per train, or pounds of coal per thousand gross 
ton-miles, are always readily available. A closer 
analysis of data which is regularly compiled 
would develop important facts which are not 
brought out in the routine reports. The head of a 
department may desire more information than 
that regularly furnished him, but he cannot take 
the time to get it himself, and a clerk could not 
understand its meaning or application, and would 



Introduction xi 

overlook important points. Great stress is laid 
on the comparison of results for successive months, 
and the comparison with figures for the corres- 
ponding months of the previous year, but statis- 
tics are no less important as a means of forecasting 
results by comparing a proposed method with the 
one in practice. The great expenditure for 
statistics is relied upon to show the leaks and 
determine wasteful methods. The field of the 
statistician should be broadened and he should 
give more attention to the possibility of con- 
structive activity. The statistical department 
has long been depended upon to keep costs from 
going up. It is time we recognize that it lies 
within its province to show how costs can be 
brought down. 

Statistics have become a vital, every-day 
need not only in transportation but also in indus- 
tries of all kinds, in finance, in journalism, in 
social work, in public life, and in business of 
every description. They are necessary to men of 
affairs, publicists, economists, and even to the 
average citizen if the significance of facts and the 
trend of events are to be comprehended. Virtu- 
ally our entire political life, both state and nation- 
al, is now regulated and its course determined by 
statistics. Every important branch of govern- 
ment has its statistical bureaus. Large financial 
institutions, industries, manufactories, railroads 
and other transportation companies have their 



xii Chartography in Ten Lessons 

statistical departments. Innumerable associa- 
tions must resort to statistics in order efficiently 
and effectively to carry on their work. 

This recent growth in the demand for reliable 
statistics and their correct interpretation has 
suddenly raised the standing of the statistician 
to one of importance, and this has been accom- 
panied by a corresponding increase in his remuner- 
ation. Today the openings for one versed in the 
fundamental laws of statistics — in their collection, 
compilation, presentation, and interpretation — 
are innumerable. The demand is greater than the 
supply. 

The value of statistics, while great, is inestim- 
ably enhanced by the aid of chartography. It 
supplements statistics — it supplies the best known 
method for their presentation and interpretation. 
In all those phases of presentation which count 
for clearness and quickness of comprehension, 
no other method is equal to it. It makes clear 
at a glance, even to the uninformed and unin- 
itiated, the significance and tendency of the fac- 
tors that are portrayed. As nine- tenths of the 
problem in interpretation is clear presentation 
the value of the service rendered to statistics 
by chartography cannot be over-emphasized. 
Especially is this realized when it is remembered 
that statistics, to be useful and valuable, must 



Introduction xiii 

not only be accurately compiled but must also be 
correctly interpreted. Relatively, too much time 
is spent in the collection and assembling of statis- 
tical material and too little in its clear and forcible 
presentation. Here is where chartography be- 
comes an invaluable handmaid to statistics. 

The graphic presentation and interpretation 
of statistics as the basis of a recognition and an 
understanding of industrial, political, financial, 
social, economic, and other tendencies has become 
essential to practical men of affairs as well as to 
publicists, economists, and others. It can be 
made of incalculable value in any line or depart- 
ment of business — in that of finance, corporate 
relations, internal organization, traffic, supplies, 
production, prices, wages, costs, and scores of 
others. It not only will repay its cost but will 
be found of such great value in so many ways 
that, once instituted, it will never be abandoned. 
It will save in the time of the busy executive alone 
more than its cost, because it will enable him to 
analyze the facts and tendencies at a glance in- 
stead of spending hours in studying the relations 
of the figures in the different columns. It will 
make more certain the correct interpretation of 
the basal information necessary to action and the 
formulation of a successful policy. It will en- 
large and extend his individual experience and 



xiv Chartography in Ten Lessons 

his accumulation of knowledge of the details and 
principles of his business. It will replace vague- 
ness and indefiniteness by assurance and certainty, 
hazy conceptions will become clear-cut perspec- 
tives, and these in turn will lead to a compre- 
hensive grasp of the entire problem. 

The recent development in and the growing 
demand for diagrammatic statistics will continue, 
and he who masters the few simple yet funda- 
mental laws or rules upon which it is based will be 
in a position to become an authority in his par- 
ticular field and to command a comfortable in- 
come. 

Frank J. Warne. 
Washington, D. C. 
October 1, 1919. 



CARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON I / 

BUILDING THE CHART 



Copyright, 1919, by F. J. Warne 

PUBLISHED BY 

FRANK J. WARNE 

SOUTHERN BUILDING 

WASHINGTON. D.C, 



CV. 



n 



©CU5 3i 



NOV -7 1919 






LESSON I 

Building the Chart 



Value of Table of Contents — Statistics and 
Chartography — Definition of a Chart — The 
Statistics — Horizontal Lines — Vertical Lines 
— A Choice of Methods — The Use of Pencil 
Dots — The Framework. 

In the Table of Contents preceding this Lesson 
has been given a comprehensive outline of the 
field the beginner in chartography is to cover in 
this and succeeding pages. It is a bird's-eye 
view of the course of study that has been mapped 
out for him- in these Lessons. It should not be 
passed over lightly but should be studied seri- 
ously, for the reason that such a study will give 
to the student at the very outset a broad per- 
spective of the problems he is to encounter and 
overcome. 

Figuratively, he is starting on a mental journey, 
with its ups and downs, its delights and pleasures, 
its perplexities and obstacles — with a good deal 
of play and some hard work ahead. The Table 
of Contents is the itinerary, kept by one who 
has many times covered the same ground and 
who thus is able to point out the significance of 

1 



2 Chartography in Ten Lessons 

the things that are to be encountered. The 
student will benefit greatly in the mastery of 
these Lessons if he will frequently re-read the 
Contents. 

VALUE OF TABLE OF CONTENTS 

The Table of Contents can also be likened to a 
railroad map in the hands of one starting on a 
long journey. It enables him to traverse with 
his eyes the entire distance of the trip, noting 
the general characteristics of the country through 
which he is to pass, its mountains and rivers, and 
the principal cities along the way. Thus he 
secures, before he starts on the journey, a much 
better idea of where he is going and becomes more 
familiar with the country through which he 
passes than he would if he studied the railroad 
map piecemeal after the journey begins. 

These ten Lessons will take the student on an 
intellectual trip in the course of which he will be 
called upon to exercise such mental traits as 
application, concentration, observation, and im- 
agination in overcoming the various obstacles on 
his way to the acquisition of knowledge concern- 
ing the art of chartography. He cannot reach 
this desirable end without progressing step by 
step in mastering its various features. And at 
every step in this progress the broad view of his 



Building the Chart 3 

final destination which he will have acquired by 
a close and frequent study of the Contents will be 
of material assistance to him. It wull not only 
enable him to cover the ground much more 
quickly and w^ith less exertion, but also with 
much more satisfaction to himself. 

STATISTICS AND CHARTOGRAPHY 

The value and usefulness of statistics and the 
relation to them of chartography, as well as the 
objects of chartography, have been pointed out 
in the Introduction. From a reading of those 
pages it should be plain that figures in tabular 
form, or which can easily be arranged in the 
form of a statistical table, are essential to the 
drawing of a chart — they are the reason for the 
chart being made. 

DEFINITION OF A CHART 

The drawing of a chart therefore presumes the 
existence of the statistics. It has nothing to 
do with their collection or compilation. A 
chart is merely a sheet of paper on which tabu- 
lated facts are presented graphically. It is 
also called a diagram or "graph." In a limited 
sense it can be likened to a moving picture, with 
this difference : In the case of the chart it is the 
eye and not the picture that moves. 



4 Chartography in Ten Lessons 

the statistics 

For the purpose of familiarizing the beginner 
with the various steps in the process of making 
the framework of a chart these figures are selected : 

1913 1914 1915 1916 1917 1918 1919 
26.7 26.7 26.4 28.1 38.2 49.5 57.2 

The first line of figures represents calendar 
years and the second line the average retail price 
of a pound of bacon in the United States on 
April 15 of each specified year. This information 
is from page 77 of the Monthly Labor Review of 
the Bureau of Labor Statistics of the United 
States Department of Labor. 

To make a chart from these figures is a simple 
proposition — as simple as the alphabet, that is, 
provided one knows the alphabet. It is as diffi- 
cult to one who does not know how as the alphabet 
is to the child first beginning to lisp the letters. 
That which at first appears to be a very com- 
plicated and difficult thing to do comes to be 
surprisingly simple after one has acquired the 
necessary knowledge and facility. In the be- 
ginning all that is needed is a lead pencil, an 
ordinary ruler, and a blank sheet of paper. 

horizontal lines 
A glance at the statistical table shows there 



Building the Chart 5 

are seven prices to be recorded. These can be 
represented for the present by as many lines 
drawn with the lead pencil at equal distances 
apart from left to right across the blank sheet of 
paper. The result gives the lines A-A, B-B, 
C-C, D-D, E-E, F-F, and G-G on this page. 



These are horizontal lines. It is important 
that the beginner bear this fact in mind. He 
should remember that a horizontal line always 



6 Chartography in Ten Lessons 

extends in the direction of the horizon, that is, 
parallel to the horizon. Here the horizon is 
represented by the top edge of the sheet. Hori- 
zontal lines are drawn from left to right, never 
from right to left. 

VERTICAL LINES 

In our statistical table we have another set of 
seven figures. These represent that number of 
years. So we mark off on the bottom horizontal 
line G-G, by means of the inch and its fractional 
units of the ruler, seven dots each an equal dist- 
ance apart, the first dot starting at the beginning 
of the line on the left. These dots we repeat on 
the top horizontal line A-A. Next we draw 
seven vertical lines connecting these dots, be- 
ginning with the first dot on horizontal line G-G. 
Upon completion of the last vertical line erase the 
dots on the top and bottom horizontal lines. 

Do not draw these vertical lines backward, 
that is, downward from line A-A to line G-G. A 
vertical line is an upright line, that is, it is 
directed perpendicularly to the plane of the hori- 
zon, as distinct from the horizontal line which, 
as has been said, is parallel to the horizon. 
These seven vertical lines we designate as H-H, 
I-I, J-J, K-K, L-L, M-M, and N-N. Superim- 
posed on the seven horizontal lines these vertical 



Building the Chart 7 

lines give the framework shown in the following 
drawing. 



M N 





















































! 























M N 



The distinction between horizontal and vertical 
lines should be clear to the student. The junc- 
tion of a horizontal and a vertical line forms a 
right angle. 



8 Chartography in Ten Lessons 

Another way to begin the erection of the frame- 
work of a chart, and one which will likely appeal 
more favorably to the student after he has ac- 
quired greater knowledge of the subject, is to 
draw first the horizontal lines G-G and A-A 
and then the vertical lines H-H and N-N. 
This gives the outline on the opposite page. 

These four lines are the really important lines 
of a curve chart. In relative importance they are 
in this order: H-H, A-A, G-G, and N-N. The 
uses to which each is put the student will become 
more familiar with in subsequent Lessons. All 
that is necessary for him to know now is that: 

Line H-H is the vertical scale line and with its 
units of measurement virtually determines the 
distance the curve is to move. In other words, 
all movements of the curve are measured by 
this line. 

Line A-A is the horizontal scale line, and in 
all curve charts involving elements of time it 
takes the time units. In our present problem 
as to the price of bacon it provides positions for 
the years. 

Line G-G is the base line of the chart. Figur- 
atively, it is the foundation line upon which all 
the vertical lines rest and from which they start. 
This base line is the zero of the vertical scale and, 
whenever possible, should always be indicated 



Building the Chart 9 

by a cipher. All movements of the curve are 
measured from this line. 

Line N-N is the least important of these four 



A 



H\ N 



A 



lines, but this is not saying that it is not necessary 
and useful. Its functions will be pointed out 
to the student later. 



10 Chartography in Ten Lessons 

the use of pencil dots 

With the four lines I have described already- 
drawn on the sheet, the beginner next divides 
by dot markings the base line G-G into six equal 
spaces, starting the first of the five dots the dis- 
tance of one space from the left end of the base 
line G-G and ending the dots the same distance 
from the right end of the base line. Duplicate 
these five dots at their respective distance apart 
on the top line A-A. Now connect these dots 
with vertical lines extending from the bottom to 
the top line. This gives the five lines I—I, J-J, 
K-K, L-L, and M-M. 

Repeat the pencil dots with the same space 
between them on vertical lines H-H and N-N, 
beginning the first of the five dots the distance of 
one space from the bottom of lines H-H and N-N. ' 
Connecting these dots with horizontal lines gives 
the lines B-B, C-C, D-D, E-E, and F-F. Now 
erase all the dot markings. The result is the 
same as that shown on page 7. 

THE FRAMEWORK OF THE CHART 

This is the framework of the chart. It is 
the scaffolding by means of which the curve is 
to be erected or constructed. It is the skeleton 
structure for supporting the curve. Without it 



Building the Chart 11 

the curve could not be constructed properly or 
correctly; neither could the curve adequately 
perform the service for which a chart is drawn. 
The lines will be found to occupy positions behind 
the curve, or rather to form a setting or back- 
ground for it. The framework is essential for 
determining the movement of the curve and 
must be built up before the curve can be placed. 



QUESTIONS FOR SELF-E XAMINATION 

1. Describe the broad view of the field of chartography 
gained from a study of the Table of Contents. What ser- 
vice does this table perform for the student? 

2. Describe the relation between chartography and 
statistics. 

3. Of what value are statistics to business? To other 
activities? What is the service chartography performs? 

4. Do these Lessons cover the entire field of chartogra- 
phy? Why? 

5. Define a chart. What is a horizontal line? A vertical 
line? How is each drawn with a pencil? 

6. What is the framework of a chart? How is it con- 
structed? 

7. What are the most important lines of the framework? 
Describe their uses. 

8. Of what use are pencil dots in drawing the lines? 
How are these dots employed in laying out the vertical and 
horizontal lines? 



12 



CARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON II 

THE SCALES OF THE 
CHART 



Copyright, 1919, by F. J. Warne 
PUBLISHED BY 

FRANK J. WARNE 

SOUTHERN BUILDING 
WASHINGTON, DX. 



£*|**t 



©CU53S4' 



LESSON II 

The Scales 
Statistical Variables — The Independent Vari- 
able — The Dependent Variable — The Horizon- 
tal Scale — Determining the Vertical Scale — 
The Scale Lines — Reading the Scales — Plotting 
the Statistics — The Use of Gradicules. 
The essence of a chart is in the relation which 
it shows exists between two or more statistical 
elements. Chartography involves a comparison. 
Probably the most frequent comparison is that 
of figures representing the trend or tendency of 
the same or similar element or factor over a 
period of time, as in the present instance of our 
statistics showing the average price of bacon on 
April 15th of different years. 

STATISTICAL VARIABLES 

This price is not the same for all the years — 
it has the capacity of changing or varying with 
the different periods of time. Thus in relation 
to each other these two groups of figures are 
called variables. 

THE INDEPENDENT VARIABLE 

A comparison being involved, one or the other 
group must be made use of as the standard by 
which the other group is measured or interpreted. 

13 



14 Chartography in Ten Lessons 

The group so used becomes the independent 
variable. Where the element of time enters into 
the situation it is nearly always the standard and 
thus becomes the independent variable. 

THE DEPENDENT VARIABLE 

The statistical group that is to be measured 
or interpreted is called the dependent variable. 
In our present problem the price of bacon being 
dependent upon the specified periods of time is 
the dependent variable. 

The relation between or the tendency of the 
units or elements of the dependent variable is 
measured by scales. One of these is the horizontal 
scale and the other the vertical scale. Generally 
the independent variable takes the horizontal 
scale. This fact is important, as a great deal of 
confusion results from a violation of this simple 
principle of chartography. 

"It should be a strict rule for all kinds of curve 
plotting," says Brinton in his Graphic Methods 
for Presenting Facts, "that the horizontal scale 
must be used for the independent variable and 
the vertical scale for the dependent variable. 
When the curves are plotted by this rule the 
reader can instantly select a set of conditions 
from the horizontal scale and read the informa- 
tion from the vertical scale. If there were no 



The Scales 15 

rule relating to the arrangement of scales for the 
independent and dependent variables, the reader 
would never be able to tell whether he should 
approach a chart from the vertical scale and read 
the information for the horizontal scale, or the 
reverse. If charts are always plotted with the 
independent variable as the horizontal scale, 
there need be no question in the reader's mind as 
to how he should interpret the chart." 

THE HORIZONTAL SCALE 

Following out this principle of chartography 
we substitute on the horizontal line A-A of the 
framework on page 7 (Lesson I), in place of the 
letters H, I, J, K, L, M, and N, the figures repre- 
senting the years in our statistical table. This 
gives the following horizontal scale line: 



1913 1914 1915 1916 !9i7 I9S8 19(9 

A i — i — i — i — r~i — r 

(H) (I) (J) (K) (L) (M) (IN) 



DETERMINING THE VERTICAL SCALE 

With the years representing the horizonta 
scale, the average price of bacon figures — the 
dependent variable — must necessarily be meas- 
ured by the vertical scale. The units of this 



16 CH AUTOGRAPHY IN TEN LESSONS 

scale are determined arbitrarily by figures that 
must have a spread sufficient to include the lowest 
as well as the highest price of bacon that is to be 
recorded according to the statistical table. The 
lowest price is 26.4 cents in the year 1915 and the 
highest is 57.2 cents for the year 1919. 

It has already been stated that the lower or 
base horizontal line is zero and should be indi- 
cated by a cipher. This also means, inasmuch 
as the vertical lines rest upon the base line, that 
the beginning or start of the vertical lines must 
be at zero. The framework above the base or 
zero line G-G on page 7 (Lesson I) provides six 
squares within which the highest number — 
57.2 — of our statistical table has to be recorded. 
With these facts to consider it is a simple mathe- 
matical computation which shows that the small- 
est unit that can be made for the vertical scale is 
that of 10 for each square. Placing this unit 
from to 60 on the vertical scale line H-H of 
the framework shown on page 7 (Lesson I) 
instead of the letters G, F, E, D, C, B, and A, 
gives the vertical scale on opposite page. 

THE SCALE LINES 

We have completed both the horizontal and 
vertical scales as determined by the figures of our 
statistical table. Substituting these scales on 



The Scales 



17 



the frame-work of our chart in place of the letters 
designating the lines gives the results shown on 
the next page. 

These scale lines — the horizontal and 
vertical — are very important features 
of a chart; in fact, without them a chart 
is unintelligible. They must be adapted 
to the arbitrary limitations of space, 
and this adaptation is readily brought 
about by increasing or decreasing the 
space allotted to each unit of each scale 
to correspond to the requirements of 
the particular statistical problem. The 
vertical scale unit itself can also be in- 
creased or decreased as the particular 
problem requires. This scale measures, 
by equal distance along all the vertical 
lines, the units of the variables that are 
being charted — it represents by space 
on the lines of the chart the equivalent 
of an agreed upon element of the statis- 
tics as determined by the units selected. 

READING THE SCALES 

The horizontal scale should read from left to 
right with the earliest year to be recorded appear- 
ing first and the remaining years following con- 
secutively in point of time. 



60 




50 





40 




30 





20 





10 







(A) 



(B) 



(C) 



(D) 



(E) 



<n 



(6) 



18 



Chartography in Ten Lessons 



The vertical scale beginning at zero should 
read upward from the bottom or base line to 
the top or horizontal scale line. 



1913 1914 t9l5 1916 1917 . 1918 1919 



60 



56 



AQ 



30 



20 



10. 



■ 










572 












49.5 










38.2 




26 7 


26 7 


264 


ze>\ 































This arrangement "faces" the chart to the 
left. A chart that faces to the right, faces in the 
wrong direction, or, putting it another way, a 



The Scales 19 

chart that does not face to the left does not face 
in the "right" direction. 

PLOTTING THE STATISTICS 

We are now prepared to begin the plotting of 
the statistics. With the vertical and horizontal 
lines drawn the proper distance apart and with the 
figures of the years and vertical scale units cor- 
rectly indicated by lead pencil marks, the student 
next begins to plot on the respective vertical 
lines, by means of pencil dots, the exact positions 
of the figures of the statistical table as determined 
by the vertical scale. 

This scale applies similarly to measurements on 
all the other vertical lines as much as it does on 
the vertical scale line itself. That is, any unit of 
the vertical scale line, say 30 of our present scale, 
has exactly the same relative position on all the 
vertical lines as it has on the vertical scale line. 

The first figure of our statistical table that is 
to be located on the chart is 26.7, representing 
in cents the average price of a pound of bacon 
on April 15, 1913. The first vertical line, which 
is our vertical scale line, also represents that year, 
as indicated by the figures 1913 at the top of the 
line. Starting at the base of this line at we 
proceed upward to 10, to 20, and somewhere be- 



20 Chartography in Ten Lessons 

tween this unit designation and the next one, 30, 
must be the proper location for the figures 26.7. 

THE USE OF GRADICULES 

It is easy to locate where 25 should be — midway 
between 20 and 30 — even without the aid of the 
slight projections or gradicules which have been 
inserted on the left of the vertical scale line in the 
chart on page 18 for the purpose of aiding the 
beginner. Each of these gradicules represents 
one-tenth of the vertical scale unit, or 1, and there 
are ten gradicules between each unit of 10. 
They perform a function similar to the sub- 
divisions of the inch unit on the ordinary ruler — 
they enable the student to locate with facility on 
the framework any figure of the statistical table 
that falls within the round numbers of the vertical 
scale units. 

With the assistance of these gradicules it is a 
simple matter to determine the correct location 
on the vertical scale line of the figures 26.7. 
This is indicated by means of a pencil dot. The 
same procedure is followed in locating on their 
respective vertical lines, as indicated by the 
vertical scale, the remaining figures for each of 
the other six years of the horizontal scale. 

The locating of each number on each vertical 
line should be done by starting at the base or 



The Scales 21 

zero line and counting upward, and not by start- 
ing from the position of the preceding pencil 
dot. One reason for this is to prevent the 
possibility of error in the location of the num- 
bers in case a mistake happens to be made in 
placing the first one on the vertical scale line. 
Besides, it is important that the beginner should 
have impressed upon his mind at the outset that 
all positions of numbers charted by means of a 
curve are determined in relation to the base or 
zero line. This is clearly indicated on page 18. 
On this drawing the numbers represented by the 
pencil dots, and which are those of our statistical 
table, are placed opposite their respective dots 
to emphasize their location. 

This presentation has prepared the student 
for the actual drawing of the curve. This he 
does by starting his pencil at the dot on the 
vertical scale line representing the number 26.7 
for the year 1913, and by means of a straight line 
marks the space between this dot and the dot 
representing 26.7 on the second vertical line, 
which latter, according to the horizontal scale, 
represents the year 1914. It so happens that the 
average price of bacon on April 15, 1914, is 
identical with the price on April 15, 1913, ac- 
cording to our statistical table. This gives a 
straight line connecting vertical lines 1913 and 



22 Chartography in Ten Lessons 

1914 at the point 26.7. The dot on the vertical 
line representing the year 1915 is at 26.4, this 
figure being the average price of bacon on April 
15 of that year. The student connects the dot 



60 



50 



1914 



1915 



1916 



1917 



1918 



1919 



40 



30 



20 



10 













/ 
































YEAR CENTS 

1913 26.7 

1914 Z6.7 




























1915 26.4 

1916 28. 1 






















1917 382 












1918 495 












1919 57.2 















representing 26.7 for the year 1914 with the dot 
at 26.4 for 1915. Continuing this process for 




The Scales 23 

In this drawing the lead pencil dots have been 
erased, as have also the gradicules along the 
vertical scale line shown in the chart on page 
18, these dots and gradicules being of no further 
use. The figures representing the price of bacon 
for the different years have also been removed 
from their positions opposite the dots and have 
been placed in statistical table form, with the 
years in the first and the prices of bacon in the 
second columns. 



QUESTIONS FOR SELF-EXAMINATION 

1. What is the essence of a chart? 

2. What are variables? What is an independent varia- 
ble? A dependent variable? 

3. What are scales? Describe the horizontal scale. The 
vertical scale. 

4. What is the relation between the variables and the 
scales? 

5. What scale does the independent variable take? 
The dependent variable? 

6. How is the vertical scale determined? 

7. What is the base line? What service does it per- 
form? What is the zero line? What is the relation between 
the lower horizontal line and the zero line? Between the 
lower horizontal line and the base line? 

8. What is a square? How is it formed? What is its 
function in chartography? 

9. What is the vertical scale unit? How is it deter- 
mined? 

10. What is a vertical scale line? A horizontal scale 
line? What relation to these are the vertical and hori- 
zontal scale units? 

11. How should the horizontal scale be read? The ver- 
tical scale? In what direction should a curve chart face? 

12. What is meant by plotting the statistics? How is 
it done? 

13. What is the relation of the vertical scale units to 
vertical lines other than the vertical scale line? 

14. What are gradicules? Of what use are they in plot- 
ting the statistics? Where are they located? Of what use 
are pencil dots in plotting the statistics? 

15. How are the positions of the figures of the statistical 
table on the framework determined? What service does 
the zero line perform in this determination? 

24 




CARTOGRAPHY 

IN TEN LESSONS 

BY FRANK J. WARNS 




LESSON III 
THE CURVE CHART 



Copyright, 1919, by F. J. Warm 
PUBLISHED BY 

FRANKJ.WARNE 

SOUTHERN BUILDING 
WASHINGTON. D.C. 



,,^ - ,-- 



,®Ci.A5 3'6 4 



NOV -7 1919 






/ 



dA 



3» 

z 



^n 



LESSON III 

The Curve Chart 



Making the Curve Heavier — The Horizontal 
Scale Unit — Squares Should be Equal — Effects 
of Different Scale Units — Dropping the Zero 
Line — Indicating the Absence of the Zero Line 
— Divisors for the Vertical Scale. 

In drawing the curve remember to make it 
heavier than any other line. The purpose of 
this is to have it stand out prominently and so 
catch and hold the eye of the reader. The 
curve should be the most conspicuous of any 
line on the chart for the reason that it embodies 
or symbolizes the most important facts that are 
presented — it is the why and the wherefore of 
the chart being called into existence. Con- 
versely, the framework lines making up the back- 
ground of the chart, that is, the horizontal and 
vertical lines, should be drawn with a lighter 
touch of the pencil to paper. 

The curve is a continuous, unbroken line, and 
has its origin at the point along the vertical scale 
line that is determined for the time or other 
designation of that line by the statistics and the 
vertical scale. It moves across the page from 
point to point on the vertical lines and in the 

25 



26 Chartography in Ten Lessons 

direction from left to right as the respective 
numbers of the statistical table determine. The 
curve terminates on the last vertical line at the 
point the statistics require. It takes the shortest 
distance between two points and generally should 
approach each slantingly. 

THE HORIZONTAL SCALE UNIT 

In a curve chart the unit of the horizontal 
scale element — in our present case this is a 
calendar year — marks a point as distinct from 
space between points. Each vertical line pro- 
jects or extends its horizontal scale unit down- 
ward all along the entire distance of that line 
even to the base or zero line. The curve cannot 
and does not affect it — the curve does not move 
any horizontal scale unit a hair's breadth from its 
place on a particular vertical line. Or, rather, 
the horizontal scale unit does not follow the 
curve from its point of contact with it on one 
vertical line to the point of contact with another 
horizontal scale unit on another vertical line. 
For instance, the year 1913 ends with the vertical 
line so designated and does not cover the space 
between vertical lines 1913 and 1914. Quite 
commonly in curve charts this distinction is 
overlooked, particularly by beginners, and the 
horizontal scale element is sometimes made to 



The Curve Chart 27 

represent space on the horizontal scale line and 
between the vertical lines. This is a mistake. 

SQUARES SHOULD BE EQUAL 

In a curve chart it is desirable to have the 
curve move from point to point in squares or 
areas of equal spacing in all directions, whether 
these be large or small. This means that both 
the horizontal and vertical scales should be deter- 
mined upon a basis that will permit equal spacing 
between the units of each scale, that is, between 
the horizontal lines of one scale and the vertical 
lines of the other. This allows the curve to move 
up or down and from left to right an equal distance 
for each unit of measurement of both scales. 

Many curve charts are being made in which this 
rule is violated. It must be added, however, that 
the observance of this principle is not always 
possible owing to the arbitrary limitations of 
space and to the necessities of the scales. The 
problem for the chartographer is to secure as accu- 
rate an observance of this rule as his difficulties will 
permit. He should constantly keep in mind the 
important fact that the horizontal and vertical 
lines are made use of to measure the quantity or 
volume or other specified quality of the statistical 
element that is charted, and that these rules of 
measurement should be as fair as possible. 



28 Chartography in Ten Lessons 

It is recommended that the beginner at first 
draw his frame work or scaffolding lines, both hori- 
zontal and vertical, exactly one inch apart, thus 
giving square inches within which the curve 
moves. Each scale will then have its units of 
measurement one inch distant from each other. 
Later on the student can practice with lessening 
or lengthening this distance, keeping in mind not 
to move the scale units to points less than one- 
half inch or further apart than one and one-half 
inches. He should not permit the units of either 
scale to be separated by any greater distance than 
the units of the other scale. 

EFFECTS OF DIFFERENT SCALE UNITS 

The student should also practice changing the 
unit of the vertical scale within the inch square, 
increasing or decreasing it to other selected units, 
in order to observe carefully the effects these dif- 
erent units have upon the movement of the curve. 
In the drawing on page 22 the unit is 10. Let us 
substitute for it the unit 5, as in the drawing on 
the opposite page. A study of these two drawings 
will disclose a number of important differences. 

Probably the most important of these is the fact 
that a vertical scale unit one-half as large, other 
factors remaining the same, doubles the space 
within which the curve moves. Conversely, 



The Curve Chart 



29 



doubling the scale unit decreases by one-half the 
distance the curve moves. 

This space in the drawing on page 22 requires 



1913 1914 1915 1916 1917 1918 19 


60 
55 
50 
45 
40 






























































JO 

30 


























?r 







vertically a fraction more than three of the 
squares — the spread in the difference between 
the lowest and highest numbers of the statistical 



30 Chartography in Ten Lessons 

table is 30.5 and with 10 as the unit this leaves 
.5 more than three times 10. In the drawing 
on the preceding page the vertical scale unit 5 
requires a fraction of . 5 more than six times 5 to 
accommodate the curve, or seven vertical squares 
at the very least. As the drawing on page 22 
provides only six squares, another one has to be 
added to the framework, as is done on the page 
preceding. This is accomplished by inserting an 
additional horizontal line, either above the top or 
below the bottom horizontal line, and then extend- 
ing to it all the vertical lines. 

With the new vertical scale unit being 5 and 
with the highest number to be charted being 
57.2 for the year 1919, a square must be provided 
for each of the units of 5 if the scale is to begin at 
zero. This demands at least twelve squares for 
the vertical scale from to 60. But it is physically 
impossible to accommodate this many squares 
of the present size within the space limitations. 

DROPPING THE ZERO LINE 

The next step is to ascertain from the statis- 
tical table the lowest number to be recorded. 
This is 26.4 for 1915. It is clear from this that 
the space occupied by all the squares below the 
vertical scale unit 25 will not be needed for record- 
ing the movement of any part of the curve, for 



The Curve Chart 31 

in not a single year of ail the seven given in the 
statistical table does the price of bacon fall below 
that unit. Consequently, beginning the vertical 
scale at 25 instead of at permits the elimination 
from the framework of five squares. The number 
that remains, which is seven, is sufficient for the 
requirements. 

It has been made clear in preceding Lessons 
that the bottom horizontal or base line of a curve 
chart represents zero of the vertical scale and is 
indicated by a cipher as follows: 



INDICATING THE ABSENCE OF THE ZERO LINE 

Such a line, of course, cannot possibly be used 
as the base line with the unit of our vertical scale 
starting at 25, so the zero designation is omitted. 
Attention should always be called to this omis- 
sion on the chart itself and this can be done by 
inserting directly below the base line, with its 
proper unit designation, a faint line of dashes or 
one of dots, or a wavy or slightly undulating 
line, as indicated on the next page. Rulers pro- 
vided with these undulations can be purchased. 



32 Chartography in Ten Lessons 



The student should keep in mind as a general 
principle the fact that the vertical scale begins 
on the base line at 0, although he will frequently 
find that this is physically impossible because of 
the nature of his statistical problem. This pre- 
vails more often among large numbers than with 
percentages. Usually the lowest number to be 
charted starts at a point so high above that the 
space required to show the latter on the chart is 
out of all proportion to that necessary to in- 
dicate the movement of the curve. Again, 
frequently in such cases the vertical scale unit 
determined by including zero becomes so large 
that fluctuations in the movement of the curve 
reflecting the trend of the statistics (which fluc- 
tuations would be made clear by the use of a 
smaller unit) are smoothed out or flattened so 
that that which should be a curve approaches 
nearer to a straight line. Thus it is not always 
possible to plot a curve chart so that the zero of 



The Curve Chart 33 

the vertical scale will be shown and at the same 
time clearly present the trend of the statistics, 
which latter is the primary object of the curve. 

In beginning to read a curve chart, among 
the first things to be observed is whether the 
vertical scale starts at zero and if it does not to 
make proper allowance for this fact in the inter- 
pretation of the movement of the curve. Unless 
this is kept in mind an erroneous idea or impres- 
sion of the extent of the movement wdll result. 
A chart that does not present the zero line and 
fails to call attention to the omission in the 
ways indicated, or neglects similar precautions, 
is constructed in error. Such a chart is very 
likely to be misleading no matter how excellent 
or perfect its other features may be. 

DIVISORS FOR THE VERTICAL SCALE 

The selection of the vertical scale unit is thus 
not without its difficulties. These the student 
will learn to overcome as his experience with 
varying statistical problems increases. He will 
learn, among other things, that particular numeri- 
cal divisors are more advantageous as units than 
some of the others. 

The divisor 3, for instance, is an awkward and 
inconvenient scale unit, not only for computing 
on the vertical lines the measurements of the 



34 Chartography in Ten Lessons 

statistical element but also for calculating by 
the interpreter of the chart. The divisor 2 is 
much better, and 5 and 10 are nearly always ideal. 
Such units as 3, 4, 6, 7, 8, and 9 are not as good as 
2, 5, 10, 20 and so on, the latter group being more 
easily divisible into the spaces along the vertical 
lines as well as into the numbers of the statistical 
table. 

Whatever scale unit is selected it must permit 
the inclusion within the arbitrary limitations of 
the framework of the smallest as well as the 
largest number that is to be charted. The unit 
must be such as to permit of a spread between the 
lowest and highest numbers charted sufficient to 
bring out clearly in the curve the points or tend- 
ency to show which the particular chart has been 
designed; at the same time it must not be too 
small as to result in exaggeration. It is as serious 
an offense to exaggerate with curves as it is with 
words. Accuracy in chart expression is as im- 
portant as is the use of words in expressing 
thought, and the various uses or functions of the 
vertical scale unit have much to do with accuracy 
in curve charts. 

On a finished chart the student will not find 
any dots and similar marks used as guides in 
erecting the scaffolding of the framework, which 
means that all such marks must be erased from 



The Curve Chart 35 

the completed chart. He will find, however, 
that all the vertical and horizontal lines make 
complete right angles at all points of junction; 
that all such lines are straight lines; that they 
form accurate squares; that the curve is slightly 
heavier than the other lines; that the scale unit 
figures are in their correct positions in relation 
to their respective lines; and that the horizontal 
and vertical scale unit figures do not crowd the 
lines but are separated from them by the correct 
spacing. 



QUESTIONS FOR SELF-EXAMINATION 

1. Why is the curve made heavier than other lines? 

2. Define a curve. How is it emphasized in comparison 
with the horizontal and vertical lines? 

3. Define the horizontal scale unit. What function does 
the vertical scale lines perform for this unit? What is the 
relation of the curve to it? 

4. What effect have unequal squares on the movement 
of the curve? What relation is there between the squares 
and the scale units? 

5. What are some of the effects of changing the vertical 
scale unit? 

6. When is the zero line omitted? How is this omission 
indicated? 

7. Explain the reasons for omitting the zero line. 

8. What effect has the omission of the zero line on the 
reading of the curve? 

9. What are numerical divisors? When and how are 
they used? What ones are better than others? 

10. What must the divisors provide for? 



36 



NOV 



CHARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON IV 

FEATURES OF A 
COMPLETE CHART 



Copyright, 1919, by F. J. Warne 
PUBLISHED BY 

FRANK J. WARNE 

SOUTHERN BUILDING 
WASHINGTON. D.C. 



V-*W<u, *■' 



©CI.A536473 



NOV -1 ^ 



LESSON IV 

Features of a Complete Chart 

The Statistical Table — Table Should Appear 
on Chart — The Make-up of the Table — Spac- 
ing the Columns — The Form of the Table — 
Duplicating the Scale Units — The Place for 
the Horizontal Scale — Word Designation of the 
Scale— The Title— The Foot-Notes— The Neat 
Lines. 

The drawing on page 38 is a complete curve 
chart constructed according to the instructions 
of the preceding Lessons. The student should 
examine carefully every one of its features. 

Particular study should be given by the student 
to the statistical table. It occupies the position 
in the lower right hand corner of the drawing on 
page 22 (Lesson II) but in the accompanying 
chart it is located in the upper left hand corner. 
In each case the location of the table is adapted 
to the requirements of the particular chart and 
each is correctly placed. It will be found that 
one or the other of these two positions is usually 
the place for the table, the lower left hand corner 
and the upper right hand corner nearly always 
being required for the free and unobstructed 
movement of the curve. 

37 



38 



Chartography in Ten Lessons 



THE AVERAGE PRICEl*OF BACON 

UNITED STATES, 1913-1919 



1913 
60 



55 



50 



45 



40 



35 



30 



25 



1913 



1914 



1915 



CENTS 
1916 



1917 



J9I8 





















YEAR CENTS 

1913 2^7 

1914 26.7 

1915 26.4 

1916 28.1 

1917 382 

1918 49.5 

1919 57.2 

























































































1914 



1915 



1916 



1917 



1918 



1919 
60 



55 



50 



45 



40 



35 



30 



25 



1919 



This simply means that there is no arbitrary- 
position on the chart for the statistical table but 
that its location is determined by the result of 
the plotting of the curve. The only general rule 
to follow is to place the table of figures in the 



Features of a Complete Chart 39 

particular position on the chart that displays it 
to the best advantage without at the same time 
crowding the scale lines or interfering with the 
curve. Breaking the vertical lines 1914 and 1915 
and the horizontal lines 45, 50, and 55, as is done 
in the accompanying chart, is not objection- 
able but rather advisable in preference to these 
lines extending through and breaking up the table. 
"Boxing" the two columns of the table with 
light lines^ as in the accompanying chart, adds to 
the neat appearance of the finished diagram. 

TABLE SHOULD APPEAR ON CHART 

Virtually every chart is based upon statistical 
information. Usually this information is in the 
form of a statistical table or columns of figures. 
If the chart has been properly constructed and if 
the figures of the table are correct, the presence 
of the statistics is not essential to a complete 
understanding of the chart — its meaning will 
be clear without the figures. Nevertheless it is 
highly important in good chart making that the 
statistics upon which the diagram is based should 
occupy an important place on the chart. 

This reproduction of the figures furnishes proof, 
if proof is needed, of the correctness of the move- 
ment of the curve as shown in the chart and will 
also be of service to those who may wish to use the 



40 Chartography in Ten Lessons 

data in other directions or to make different com- 
pilations. Unless the statistics from which the 
chart is made are shown upon it there is no easy 
way to check up the work of the chartographer. 

THE MAKE-UP OF THE TABLE 

The internal make-up and arrangement of the 
statistical table also require some thought from 
the student. Its construction would appear, at 
first glance to be an easy thing to do and yet the 
task has its difficulties. 

All the numbers of the same statistical element 
that are to be compared should be placed in the 
same vertical column one under the other and not 
too far apart, the digits of the tens and hundreds 
and so on occupying their proper positions in 
relation to similar digits of other numbers in the 
same column. In the case of years, these are ar- 
ranged vertically and in proper sequence of time 
one under the other with the earliest year at the 
top and the latest year at the bottom of the col- 
umn. Nearly always the years are in the first 
column to the left in a table of two or more col- 
umns. Vertical columns of figures read downward 
from the top and never upward from the bottom. 
This is in inverse order, it will be noted, to the 
reading of the vertical scale units. 

Each column has its proper word designation 



Features of a Complete Chart 41 

just above the first number, as years and cents in 
the table of the chart on page 38. This is the 
column heading. The space for- it is usually very 
limited and for this reason it should be confined to 
simple words of the fewest possible letters con- 
sistent with clearness as to the meaning of the 
column of figures. Double meaning of words 
should be as carefully guarded against as indefin- 
iteness in meaning, each being a serious offense 
against clearness of expression. When two or 
more words are necessary in the heading of a 
column it is usually advisable to make of them 
two or more lines just above the first number, 
with each word having a line to itself instead 
of all the words occupying a single line, which 
latter nearly always extends the heading too far 
on either side of the column of figures. 

SPACING THE COLUMNS 

Where two or more columns of figures are in 
the same table attention has to be given to the 
proper spacing between the columns as well as 
between the numbers themselves and their 
headings. But in every table the number of 
columns should be strictly limited to the fewest 
possible for the purpose in view, the inclusion of 
any that are not necessary detracting from the 
emphasis that must be given to the principal 



42 Chartography in Ten Lessons 

facts and tendencies shown by the statistics. The 
table must be complete in itself, however, with no 
vitally important factor missing. To this end 
more than one comparison should not be at- 
tempted in the same table. 

The form of the table has to be adjusted not 
only to the size of the chart but in particular to 
the space available on the framework for its 
presentation without interfering with the curve. 
Interference by the table with the light horizontal 
and vertical lines is not so important; nor is a 
correct interpretation or reading of the curve 
interfered with even when the vertical scale line is 
broken into by the table at points which the curve 
does not approach. 

THE FORM OF THE TABLE 

There are distinct forms best adapted to par- 
ticular purposes with which the student will be- 
come familiar only by practice. He will have to 
decide at times whether he will include all his 
data in one table or break them up into two or 
more tables with a chart to illustrate each. Com- 
pactness as well as proximity of the numbers for 
comparative purposes are advantages which 
must sometimes be surrendered at the demand of 
more pressing requirements. If the table is too 
large confusion to the eye results and difficulty is 



Features of a Complete Chart 43 

encountered in following the significance of the 
separate columns. Interpretation also is particu- 
larly taxing if the tabulation is dealing with a 
complex mass of figures. 

SIMPLICITY THE GUIDING RULE 

If the student will keep in mind that simplicity 
must be the guiding rule he will usually not go far 
wrong in his decisions. Much, of course, depends 
upon the data that must be shown but quite often 
more can be eliminated from the columns than 
at first seems possible. Foot-notes as explanations 
of the table often show a way out but these should 
be kept at the minimum. A title to the table 
separate from that of the chart is unnecessary. 

Sometimes the exigencies of space limitations 
combine with the requirements of the movement 
of the curve to prevent the use of the form of 
statistical table that has been described and which 
is shown in the chart on page 38. In such cases 
recourse has to be had to some other form, some- 
times to that shown on page 4 (Lesson I) with 
the years and prices of bacon arranged in hori- 
zontal lines instead of vertical columns. At 
times when this form has to be resorted to it is 
not possible to place the table within the frame- 
work and in such cases a position has to be found 
for it elsewhere on the chart. 



44 Chartography in Ten Lessons 

duplicating the scale units 

In the chart on page 38 the unit figures of the 
horizontal scale have been placed on both the top 
and bottom lines and those of the vertical scale 
on both the first and last vertical lines. This 
arrangement has many advantages. While it 
is not essential to the reading of the curve, at 
the same time it facilitates the interpretation of 
its movement in that the reading of the prices 
of bacon for the first and immediately succeeding 
years is permitted without requiring the eyes to 
move upward to observe these horizontal scale 
units; also, it permits the quick reading of the 
prices of bacon for 1919 and the immediately 
preceding years without requiring the eyes to 
travel across the page to observe these particular 
vertical scale units. The scale units arranged 
along all four sides also serve to give a border- 
like appearance to the framework and introduce 
a little greater uniformity in place of a tendency 
towards a lack of balance. 

THE PLACE FOR THE HORIZONTAL SCALE 

Some chartographers prefer placing the hori- 
zontal scale units along the bottom line only. 
My own preference is that where they are to 
appear only once on the chart then the place 



Features of a Complete Chart 45 

for them is on the top line. That line will be 
found to be much more convenient as the hori- 
zontal scale line; besides, there are other im- 
portant uses for the bottom horizontal line, such 
as serving as the base line and as the zero line. 

This preference is influenced also as the result 
of more than ten years' experience in chart 
making for practical commercial purposes. Dur- 
ing this experience it has been observed that most 
people in reading a chart start at the top with 
the title and glance downward. With the units 
of the horizontal scale on the top line the reader 
early in the process of interpretation is informed 
of these important facts which he must know if he 
is to read the chart intelligently and correctly. 

Placing the horizontal scale units on the bottom 
line meets with the objection that the space 
beneath this line is usually needed in most curve 
charts for important explanations and foot- 
notes, such as credit for the source of the statis- 
tical information upon which the chart is built, 
notice of copyright, and so on. With the hori- 
zontal scale figures also there that section of the 
chart is likely to give the appearance of crowding. 

Again, with the horizontal scale figures located 
on the bottom line I have frequently encountered 
practical difficulties hard to overcome because 
the first and last of these units interfere with 



46 Chartography in Ten Lessons 

those of the lowest scale measurement of the 
vertical lines, both sets of figures being located 
at nearly the same point of the right angles formed 
by these vertical and horizontal lines. As op- 
posed to this, it is nearly always possible to extend 
the upper part of the framework at least one 
series of squares beyond the highest point to be 
recorded by the vertical scale and this permits 
the figures of the horizontal scale units to have a 
line all to themselves without interfering with and 
without interference from any of the figures of the 
vertical scale. 

There is no objection, of course, to reproducing 
the horizontal scale figures on the bottom line 
whenever there is room for them, and this prac- 
tice is recommended as being advantageous, 
especially in charts of unusual depth, as it facili- 
tates a quick reading of the curve movement. 

WORD DESIGNATION OF THE SCALE 

Further assistance in the interpretation of the 
chart, and especially in the reading of the curve, 
is rendered if the primary characteristic of the 
statistical element represented by the vertical 
scale is indicated by a word designation just 
inside the top border line and directly above the 
center of the horizontal scale line. This is shown 
in the designation "Cents" in the chart on page 



Features of a Complete Chart 47 

38. Such a designation states concisely to the 
reader what the vertical scale figures represent— 
it explains the essence of the curve. Its value 
and usefulness will be impressed upon the student 
as he progresses in his studies. 

the title 

Another important matter to be considered 
before our chart is a complete one is the title or 
heading. Every chart must have a title. With- 
out it the chart is almost as incomplete as it 
would be if the curve itself were omitted. The 
title is as much a part of the chart as are the 
scale lines or table of statistics. It is more im- 
portant than the beginner in chart making is 
apt to realize. 

The title should not contain a single unneces- 
sary word. The space for it is usually limited 
and too many words detract from the effect in 
expressing the idea intended. Simple words of 
one syllable are preferable. This choosing of 
words in the selection of a title is a splendid 
exercise in enabling one to secure a better com- 
mand of the English language and in compre- 
hending more clearly himself the essence of the 
chart. The title should be so clear in its meaning 
that misinterpretation is impossible, and so com- 
prehensive in its scope as to cover all the import- 



48 Chartography in Ten Lessons 

ant data presented by the chart so that the inter- 
preter will not have to look elsewhere for explana- 
tion. This is not always possible and in such 
cases a foot-note explanation at the bottom of the 
chart is advisable. Indefiniteness in title mean- 
ing is a serious offense. Similar statements are 
equally applicable to any sub-title. 

The position of the title is, of course, at the 
top or head of the chart, as shown on page 38. 
The best title is one comprising a single line but 
this is not always easy to accomplish. In the 
chart referred to it has been found necessary to 
have two lines in the title, and in such cases the 
letters of the words in the second line should be 
slightly smaller than those of the first line. The 
principal idea in this chart is the tendency in the 
price of bacon, so its title becomes "The Average 
Price of Bacon." But as this does not give the 
information quite complete enough, the reader is 
told in the second line that the price is for the 
entire "United States" and for the years "1913 
to 1919." The asterisk after the word "price" 
refers the reader to the foot-notes, where it is 
stated that the average price given is of April 
15 of each year. 

THE FOOT-NOTES 

The place on the chart for the foot-notes is 



Features of a Complete Chart 49 

just below the base line and outside the frame- 
work proper. These serve a useful purpose in 
presenting descriptive information sometimes 
necessary to clear up a point that has not been 
brought out sufficiently in the chart, as indicated 
in the use of the asterisk in the chart on page 38. 
In the foot-notes there should always be a state- 
ment as to the source of or authority for the 
statistics upon which the chart is based. This 
is shown on the chart just referred to by the 
notation "Statistics are from Monthly Labor 
Review, p. 77, U. S. Bureau of Labor Statistics." 
The foot-notes also supply a convenient place for 
the legal statement required in case the chart is 
copyrighted. 

THE NEAT LINES 

With the drawing of the border or "neat" lines, 
one on each side of the framework and usually 
about one-half an inch from the horizontal and 
vertical scale lines, the chart is completed. These 
neat lines give a sort of frame to the chart, as 
shown on page 38. 

In a good curve chart the principal conclusions 
to be drawn from the statistical table are made 
plain, all doubt as to the tendency or course of the 
phenomena represented by the numbers is re- 
moved, and all possible errors have been elimi- 



50 Chartography in Ten Lessons 

nated. This ability to analyze the significance 
of a table of statistics, to interpret the results 
correctly and clearly, and to indicate the con- 
clusions lucidly and succinctly is one of the 
characteristics of chartography. The results 
disclosed by a curve based upon a statistical table 
quite often reveal at a glance important facts 
that could not have been known except from 
considerable study of the figures by an expert. 
Usually an accompanying explanation or analysis 
is unnecessary. If so the chart has failed of its 
primary purpose. 

The task of checking-up is not optional with 
the student; it is compulsory — he not only should 
but he must go over carefully each chart from top 
to bottom. 

If it is a curve chart, do all the horizontal scale 
units center on the end of the vertical lines? 

Are the respective vertical scale units on the 
right in the curve chart directly opposite and at 
the end of the same horizontal line as those on the 
left? 

If the curve chart contains a zero or 100 per 
cent line, has it been made wider or heavier than 
the other horizontal lines? If the zero line is 
not shown, does the bottom or base line clearly 
indicate that the vertical scale does not begin 
with zero? 



Features of a Complete Chart 51 

If it will aid in the easy reading of the curve see 
that the horizontal scale figures are duplicated at 
the base line. 

In most curve charts it is best to have the 
vertical scale figures on the right as well as on 
the left vertical scale line. If only one set of 
scale figures are used, however, these should be 
alongside the first or left vertical line. 

Do not make use of the first and last vertical 
lines of a curve chart as the neat lines of the frame. 
They should be reserved strictly for the vertical 
scale units and should be no heavier or wider than 
the interior vertical lines. 

Do not forget that it is the independent variable 
that takes the horizontal scale, especially in 
curve charts involving periods of time. 

Follow each curve from its beginning on the 
left to its termination on the right to see that it is 
continuously correct — that there is no "break" 
in it. See to it also that the curve is a slightly 
heavier line than the vertical and horizontal 
lines. 



QUESTIONS FOR SELF-EXAMINATION 

1. Describe in general terms the most important char- 
acteristics of a curve chart. 

2. What is the statistical table? What is its relation to 
the curve? 

3. What is the position of the table on the chart? What 
are its general features? What is meant by "boxing?" 

4. What is the internal make-up of a table? What is a 
column heading? What is meant by spacing? 

5. What is the guiding rule in table construction? 

6. What features of the chart affect the form of the 
table and its position on the framework? 

7. What is meant by duplicating the scale units? How 
is this done? What are the advantages? 

8. What is the position for the horizontal scale? Give 
reasons supporting your statement. 

9. What is the function of the word designation of the 
vertical scale? 

10. What is the title? What is its location? Describe 
the principles underlying the selection of words for the 
title. 

11. What is an asterisk? What are its uses in chartog- 
raphy? 

12. What service do foot-notes perform? Where are 
they located on the chart? What do they usually comprise? 

13. What are neat lines? What is their position on a 
chart? 



52 



CHARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON V 
THE BAR CHART 



Copyright, 1919, by F. J. Warne 
PUBLISHED BY 

FRANK J. WARNE 

SOUTHERN BUILDING 
WASHINGTON. D.C. 



•/ 



2CI.A58 6 



NOV -1 i9l9 




4A 



3\ 



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% 



LESSON V 

The Bar Chart 



Making Bars from a Curve — Making a Curve 
from Bars — Advantages of the Horizontal Bar 
— Reversing the Scales — Width of the Bar — 
Separation of the Bars-— Location of the Table 
— The Bar and the Curve. 

Emphasis thus far has been placed on the curve 
as the method of expression offered by the art of 
chartography. But there is also the bar. Many 
of the principles of construction already explained 
in describing the curve apply with equal force 
to the bar chart. In fact, there are many points 
of similarity between these two different kinds of 
charts, 

MAKING BARS FROM A CURVE 

This the student will be able to realize clearly 
by taking a curve chart and drawing vertical 
bars from its base line to the points of the curve. 
This has been done in the chart on page 54. It 
is merely the result of taking the curve chart on 
page 38 (Lesson IV) and with as few changes as 
possible transforming it into a bar chart. 

In order to secure a bar for each of the seven 
years it is necessary to add another vertical line 

58 



54 



Chartography in Ten Lessons 



to the right of the one for the year 1919 and 
extend to it the top and bottom horizontal lines. 
The horizontal scale unit for each year is moved 
to the right from its former position at the top 




1913 



916 1917 1918 1919 



of a vertical line so as to occupy space between 
the vertical lines and to be above the top of the 
bar. No change is made either in the unit of 
measurement of the vertical scale or in its location. 



The Bar Chart 55 

making a curve from bars 

This procedure enables the many points of 
similarity between the curve and the bar chart 
to be quickly recognized. This similarity will 
all the more be indelibly impressed upon the 
mind of the student if he will take the vertical 
bar chart on page 54 and draw a continuous 
curve from left to right touching the tops of all 
the bars. Then if he will cut out a piece of blank 
paper so that its upper edge conforms roughly 
to the curve he has drawn he will find, by placing 
this on the bars, that the latter are hidden from 
view and that the curve remaining in sight ex- 
presses just as clearly the tendency shown by the 
bars. In other words, his cut piece of blank paper 
has simply restored the original curve chart on 
page 38 (Lesson IV). 

This procedure also emphasizes strikingly the 
essential difference between these two kinds of 
charts. This difference lies primarily in the fact 
that the horizontal scale of a curve registers points 
on lines while the horizontal scale of a vertical 
bar chart registers space between points on lines. 

But in changing the curve to the bar we have 
not secured a good bar chart. In the first place 
the bars are entirely too wide to represent such 
small amounts as cents. In the second place the 
bars take up entirely too much space — the same 



56 Chartography in Ten Lessons 

ends can be accomplished by the use of a narrower 
bar. In the third place the result is a vertical 
bar, that is, a bar standing upright on its end. 
A horizontal bar, that is one lying on its side and 
extending from left to right, is preferable. 

advantages of the horizontal bar 

This preference is based on an experience of 
years in meeting the every-day problems of 
chartography. It convinces the writer of the 
greater utility of the horizontal bar. Quite 
probably there are occasions when it is advisable 
to have recourse to the vertical bar, but at the 
same time where there is a choice between the 
two the horizontal bar will be found to be more 
advantageous. It gives greater opportunity for 
the display of letters and figures where the limita- 
tions of space or other considerations require that 
these be placed on the bars themselves. In 
such instances, in order easily to read the words 
or figures on vertical bars the chart usually has 
to be turned half way round to the right, whereas 
if the bars are horizontal the figures and letters 
read in the natural direction. In brief, with the 
vertical bar the chartographer will encounter more 
difficulties than with the horizontal bar in the 
placing of his table, figures, and letters. The 
ability to select advisedly in those cases where it 



The Bar Chart 57 

might be advantageous to employ the vertical 
bar will come to the student with practice and 
experience. It is recommended that in the mean- 
time he confine himself to the practice of the 
horizontal bar. 

Such a bar chart is presented on the following 
page. It will be observed, from a comparison 
of its statistical table with that of the curve chart 
on page 38 (Lesson IV), that it is constructed 
from the same set of figures. 

REVERSING THE SCALES 

The horizontal bar has necessitated a reversal 
in the location of the scales in comparison with 
those of the curve. Instead of the independent 
variable — the years — occupying the horizontal 
scale position it takes that of the vertical scale, 
and the dependent variable — the prices of bacon 
— becomes in turn the horizontal scale. This 
permits of the measurement of the movement of 
the bars from left to right and not from the bottom 
up, as with the vertical bar. Otherwise we could 
not secure the advantages of the horizontal bar. 

In a horizontal bar chart the figures of the 
vertical scale, quite frequently comprising periods 
of time, are located directly to the left of the 
beginning of the -bars, the figures for each year 
being centered adjacent to their respective bar. 



58 



Chartography in Ten Lessons 





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The Bar Chart 59 

The last digit of the number should not be per- 
mitted to crowd the end of the bar too closely. 

WIDTH OF THE BAR 

It will be noted that the bars are narrower 
in the chart on page 58 than in the one on page 
54. This feature of the bar is important. Just 
how narrow or how wide or deep the bar should be 
will depend upon a number of factors, such as 
the nature of the particular statistical problem, 
the arbitrary limitations of space, and so on. No 
definite rule can be given except that all the bars of 
a chart must be of uniform width, they should be 
sufficiently wide to be easily seen, and they should 
convey an impression of the volume or quantity 
represented. For instance, a bar representing 
billions should be wider than one representing 
millions; the latter wider than one representing 
hundreds of thousands; and the latter of greater 
width than one representing thousands, and so on. 
Wide bars are preferable to too narrow ones. 

In beginning to draw the bars the student 
should indicate on the sheet by light lead pencil 
lines instead of dots the width and length of each 
bar, the former being arbitrarily determined by 
the number of bars that is to go in the available 
space and the latter by the quantity or volume 
each bar represents as determined by the statis- 



60 Chartography in Ten Lessons 

tics and the scale unit. It is first advisable to 
determine from the statistics and the horizontal 
scale unit the length of the shortest and the 
longest bar. All the other bars fall within the 
limits these two set. Begin plotting the chart 
with the bar for the earliest year at the top and 
just beneath the horizontal scale line, outlining 
the bars downward as the years determine. These 
skeleton bars should then be filled in black by 
rotating the pencil point within the outlines. 

SEPARATION OF THE BARS 

Between each bar representing the statistical 
element of the vertical scale there should be a 
separation sufficient to distinguish it from the 
preceding and following bar. In the chart on 
page 58 this has been done by leaving in the 
original drawing a space equal to one-tenth of an 
inch. Usually this is too much spacing. Besides, 
it requires a greater amount of painstaking labor 
than should ordinarily be given to a bar chart. 
How this labor can be eliminated the student will 
be informed in a succeeding Lesson. 

The bar chart on page 58 shows the vertical 
lines extending from the points of the scale 
units on the top horizontal line to the base hori- 
zontal line except where the bars and the statis- 
tical table intervene. These extend downward 



The Bar Chart 61 

the units of measurement of the horizontal scale 
to each of the seven bars at the various points of 
contact of the vertical lines with the bars. Ordi- 
narily these vertical lines should not be extended 
between the bars but to the first bar only that 
interferes with their further extension. These 
lines are permitted to be seen on this chart merely 
to inform the student as to the purpose of the 
vertical lines in a bar chart. All sections of verti- 
cal lines that have been drawn within the bars 
should be pencilled out of observation as the body 
of the bar is pencilled in. 

LOCATION OF THE TABLE 

The location of the statistical table in the upper 
right hand corner is that which will usually be 
found best adapted for this use. This is true be- 
cause this position, as a general thing, is opposite 
the shortest bars and thus has the largest area of 
unoccupied space. The lower right hand corner 
is frequently taken up with the extension of the 
longest bars representing the largest numbers 
to be charted, and the upper and lower left hand 
corners always contain the beginning of the bars. 

In cases where the extensions of the bars from 
the earliest to the latest years show a decrease 
instead of an increase, the statistical table should 
be located in the lower right hand corner. The 



62 Chartography in Ten Lessons 

table should be "boxed," that is, enclosed in a 
light frame composed of two vertical and two 
horizontal lines connecting at their ends and form- 
ing right angles. 

Separating the numbers from their table and 
placing them on the individual bars adjacent to the 
figures of the years will sometimes be found advan- 
tageous. 

THE BAR AND THE CURVE 

As between the bar and the curve chart the 
latter will be found to be much more useful as 
well as more adaptable to a larger number of statis- 
tical tables or problems. It is true that in many- 
instances either may be employed with equally 
successful results. The bar chart, however, is 
the most common at the present time not only 
because it is the simplest to construct but also 
to interpret. Its advantage lies in its simplicity — 
the amount or quantity or statistical element is 
simply represented by the length of the bar. This 
gives only one dimension to be read and in conse- 
quence there is little ground for misinterpreta- 
tion. As a general statement the bar method 
should be used where the numbers represent large 
volumes or quantities. 

At the same time there are special problems in 
chartography w^hich the curve chart alone will 



The Bar Chart 63 

solve to the best advantage. Just what are the 
particular characteristics of these problems the 
student will learn by experience. The kind of 
chart that will best bring out the true significance 
of a statistical table is the one to select. It can be 
said generally that with statistical tables having 
numbers representing very large amounts, such 
as billions and millions, the bar chart is preferable. 
Conversely, where the numbers represent small 
amounts, such as hundreds and tens, the curve 
chart is usually the best. One reason for this is that 
the bar conveys the idea of volume to a greater de- 
gree than does the curve. 

The difference between these two kinds of charts 
is strikingly presented by Brinton in his Graphic 
Methods for Presenting Facts. He first com- 
pares bars representing years or other intervals of 
time with progress photographs. Though the bars 
and progress photographs are valuable, he says, 
they give information only in spots. Then he says : 

"A moving-picture machine shows pictures so 
rapidly that the pictures blend into a continuous 
narrative in the eye and the brain of the observer. 
What the moving-picture is to separate progress 
photographs, the curve is to detached bars repre- 
senting time. In just so much as the moving-pic- 
ture is sliperior to separate pictures shown by 
lantern slides, in just that much is a curve superior 



64 Chartography in Ten Lessons 

to a series of horizontal or vertical bars for the 
same data. Unless a person knows thoroughly 
how to read and how to plot curves he cannot 
hope to understand the graphic presentation of 
facts." 

Brinton also says: "A curve permits of finer in- 
terpretation than any other known method of 
presenting figures for analysis — it gives informa- 
tion which many persons might not fully grasp if 
only a column of figures were used." And again 
the same author says: "One of the chief advan- 
tages of the curve method of presenting informa- 
tion is that a curve forces one to think." 

It will be found that plotting the curve is sim- 
pler than plotting the bar. It also consumes less 
time. Many chartographers prefer the curve to 
the bar method of presenting statistics because 
it not only brings out the fluctuations from year 
to year more clearly to the eye but also enables 
the reader to grasp more readily the tendency 
shown. The curve is gradually supplanting the 
bar in popular usage because of its greater clear- 
ness, and this tendency is likely to grow stronger 
as its advantages over the bar are more generally 
recognized. 

QUESTION FOR SELF-EXAMINATION 

1. Describe the similarities and differences of the curve 
and bar chart. 



NOV 



; ■■; 



CHARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON VI 

THE TOOLS OF THE 
CHARTOGRAPHER 



Copyright, 1919, by F. /, Warne 
PUBLISHED BY 

FRANK J. WARNE 

SOUTHERN BUILDING 
WASHINGTON, D.C. 



)CI.A536f73 



-7 i9i9 



M*i 



\4% 



*n 



LESSON VI 

The Tools of the Chartographer 

Cross Section Paper — The Lead Pencil — The 
Kind of Ink — The Ruling Pen — Correct Posi- 
tion for Holding Pen — Pen Points — The Draw- 
ing Board — The T- Square — The Triangle — 
The Engineer's Scale — The Dividers — The 
Essential Tools. 

If the beginner has profited to the full extent 
from a careful and painstaking study of the pre- 
ceding Lessons he is now qualified to drop the 
blank sheet of ordinary paper, the lead pencil, 
and the common ruler and take up the real 
materials and tools of the chartographer. The 
proper use of these materials and tools will 
measurably facilitate and make less difficult 
the mechanical work of chart making and will 
also result in much better workmanship. It 
permits of the chart becoming permanently 
valuable as well as of its reproduction in any 
number desired. 

cross section paper 

The most important of the essential materials 
is the cross section or coordinate paper. A 
sample illustration is shown on the following 

65 



Tools of the Chartographer 67 

page. This section paper comprises minute 
squares formed by horizontal and vertical lines. 
On the most commonly used section paper each 
minute square measures one-tenth of an inch. 
One hundred of these squares make up a larger 
square of one inch, the border lines forming the 
square inch being slightly heavier than the other 
horizontal and vertical lines. Section paper can 
also be secured that has other rulings, such as 
eight minute squares each way or sixty-four to 
the square inch, and six each way or thirty-six 
to the square inch. 

Cross section paper thus presents a system of 
squares whose lines permit the easy measurement 
or determination, by means of space or distance 
on the sheet, of the quantity or volume or what- 
ever element it is the statistical table represents. 
By combining squares, space units of measure- 
ment as extended in both directions as the par- 
ticular problem requires are readily determined. 

A sufficient quantity of section paper for most 
charting purposes can be obtained at almost any 
first-class stationery store. If a large number of 
different charts is to be made the varying scales 
will likely require different subdivisions of the 
square inch and as it requires too much detail 
labor for the chartographer himself to draw these 
subdivisions, it is advisable for quantity produc- 



68 Chartography in Ten Lessons 

tion to keep on hand a supply of coordinate 
sheets with the different rulings. Even then the 
chartographer will not always have paper with 
the ruled spaces exactly corresponding to his 
requirement, and in such cases he will have to do 
the ruling himself. 

In sheet sizes the section paper is usually 17 
by 22 inches. These sheets can be cut to meet 
almost any ordinary requirement; or two or 
more can be pasted together along the edges to 
meet the demand for a larger surface than that 
commonly required. Built-up sheets of paper can 
also be formed from remnants by pasting. If a 
larger section-ruled surface than 17 by 22 is 
frequently required it will be advantageous to 
purchase the coordinate paper in rolls, in which 
form it is also prepared commercially. 

The section paper used should be of the best 
quality. There are cheap grades on the market 
but these do not take the ink satisfactorily and 
have other defects, so that in the long run it pays 
to purchase the better grade at little higher 
prices. Of course, a higher price does not neces- 
sarily mean a better grade, but it usually does. 

The section paper best adapted to ordinary 
chart work has the horizontal and vertical lines 
ruled in blue ink. On some section paper these 
lines are in green or purple but these colors are 



Tools of the Chartographer 69 

not so desirable, as they are likely to reproduce 
lines on the photographed chart that should not 
be shown. Paper with a soft surface should 
also be avoided as it will not take the ink properly, 
and from now on we are to make all our charts 
with pen and ink instead of pencil. 

THE LEAD PENCIL 

This does not mean that the student will have 
no more use for the lead pencil. In fact, he will 
continue to have constant need of it. The lead 
should >e neither too soft nor too hard — it should 
not be so soft as to crumble, or so brittle as to 
snap in two or so hard as to penetrate or puncture 
the drawing sheet. The best grade for general 
use is HB. 

Virtually all points of measurement, such as 
the distances from unit to unit of the scales and 
those of the curve and each bar, should first be 
indicated on the section sheet by light lead pencil 
marks or dots. This use of the dots will facilitate 
the drawing of the lines, curve, and bars in ink. 
The entire curve and an outline of each bar might 
with advantage first be drawn in light lead pencil, 
the ink being later superimposed after the student 
has satisfied himself that his pencil markings 
correctly represent the data. The dots and other 
lead pencil markings can be erased after the ink 



70 Chartography in Ten Lessons 

has dried. It is much easier to correct a mistake 
made in lead pencil than one made in ink. The 
curve itself is made finally with the draftsman's 
ruling pen. The neat lines of the frame are 
drawn in ink after the framework of the chart has 
been entirely completed. 

THE KIND OF INK 

The best black ink for charting purposes is 
Higgins' American India. In purchasing ask the 
dealer for waterproof quality. This, when it 
dries, is insoluble and will not smear or spread in 
case the sheet is brought in contact with water, 
as is often the case when the chart is to be re- 
produced by the blue-printing process. Another 
favorable quality of this ink is exhibited in the 
process of drying areas on charts, such as bars, as 
it dries with a flat or "dead" surface. Such a 
surface is highly desirable in case the chart is to 
be reproduced by such photographic processes 
as zinc-etching, photo-lithography, and so on. 
"Chin-chin" ink, also an India ink and noted 
for its opacity, can be used to special advantage 
in cases where the chart is to be reproduced by the 
blue-printing process. While special mention is 
made of these two inks, there are also other India 
inks on the market equally as good for ordinary 
charting purposes. With the smaller bottles is 



Tools of the Chartographer 71 

usually supplied a beveled quill inserted in the 
cork which is used in filling the ruling pen. 

THE RULING PEN 

This ruling pen is an invaluable tool to the 
chartographer. It has two blades or tines the 
relation of each to the other being controlled by 
an adjusting screw. The manipulation of this 
screw permits the drawing of lines of varying 
widths. The use of the ruling pen should be con- 
fined to line and curve work. Some pens have a 
lever attachment which permits the cleaning of 
the tines without disturbing the gauge at which 
they may be set. This lever saves the time re- 
quired to make the proper adjustment again and 
prevents the possibility of the chartographer 
resuming work with a different adjustment of the 
tines. 

CORRECT POSITION FOR HOLDING PEN 

The ruling pen should be held in such a position 
as to be in a plane perpendicular to the surface 
of the drawing sheet, the tips of the thumb and 
forefinger grasping the pen at the adjusting 
screw. This is illustrated on the following page. 

Holding the pen in this way permits, when 
necessary, the manipulation of the screw by 
slightly raising the pen from contact with the 



72 



Chartography in Ten Lessons 



sheet. In ruling lines or curves the hand or 
fingers should not touch the paper, nor should 
the elbow rest on the sheet. The movement of 




the pen is not from the hand but is a free elbow 
movement and is from left to right and from bot- 
tom to top of the sheet. 



Tools of the Chartographer 73 

Failure to observe these instructions will result 
in the points of the tines wearing away unevenly 
and the pen then develops what is referred to by 
draftsmen as a "shoulder." This usually means 
that this particular pen must be discarded for 
line and curve work as it is no longer a "true" 
instrument or tool. These old pens can be used to 
advantage, however, in filling in bars, they being 
operated in such cases somewhat as one would a 
small brush. It is not impossible to remove a 
"shoulder" from a ruling pen. This can be done 
by using a small oil-stone or razor-hone. The 
stone or hone can also be used to advantage in 
keeping the points of the tines sharp and true. 
In this process of sharpening be careful to hold 
the ruling pen against the surface of the stone or 
hone at an angle of about forty-five degrees, 
grinding the points with a gentle rotary motion. 
Follow this by rubbing the points of the tines on 
any glass surface. An examination of the 
points should then find all "burrs" or unevenness 
to have been removed. 

PEN POINTS 

In addition to the ruling pen and as a substitute 
for it in many uses, the student will need pen 
points and, of course, a penholder or holders. 
For fine line work and small lettering Gillett's 



74 Chartography in Ten Lessons 

No. 303 is recommended. Esterbrook's No. 14 
bank pen point is also good for lettering, Gillett's 
No. 291 will also be found satisfactory, especially 
in mapping work. 

The student is no doubt familiar through per- 
sonal experience with the fact that most pen 
points when first dipped in ink repel or throw off 
the ink. This is likely to result in blots or spots 
if it occurs on a sheet of drawing paper. To 
obviate this it is suggested that the pen point be 
held for a moment in the flame of a match before 
being put to use for the first time. 

THE DRAWING BOARD 

The effective use of the section paper, the pen- 
cil, the ruling pen, the pen points, and the ink 
makes necessary that the student also have a 
drawing board. This is nearly always made of 
neatly glued strips of soft wood, usually white 
pine, with a hardwood ledge of an inch or so on 
each end. The board can be secured in varying 
sizes ranging from 12 by 17 inches to 31 by 42 
inches. Larger sizes can also be purchased. The 
board rests unattached on the desk or table and 
can be moved about freely with the section paper 
temporarily attached to it by means of thumb 
tacks. In case the student prefers a drawing table, 
this can be had in various makes and designs. 



Tools of the Chartographer 15 

the t-square 

The drawing board or table facilitates greatly 
the use of the T-Square, another tool of the char- 
tographer which he will find invaluable. It is 
so-called because of its resemblance to the cap- 
ital letter T. For all purposes of accurate line 
drawing not involving measurement it supplants 
the ordinary ruler. A T-Square fitted with trans- 
parent ruling edges is recommended, as it permits 
the draftsman to see adjacent portions of the 
section sheet that would be hidden if a wooden 
straightedge were used. It fits in snugly and 
along either ledge of the board or table accurately 
by reason of the head piece of the T-Square ex- 
tending beneath the blade with its ruling edges. 
This permits of a true base line as well as other 
horizontal lines. Upon this base line, with the T- 
Square in position, true vertical lines are erected 
by means of the Triangle. 

THE TRIANGLE 

The use of the Triangle is largely confined to 
making vertical and horizontal lines. Do not 
attempt to draw these lines with the ordinary 
ruler if any degree of accuracy is desired as such 
an attempt will most likely result in inaccuracy. 
Accuracy, it should be remembered, is one of the 
cardinal principles of good chartography. 



76 Chartography in Ten Lessons 




ne. 1 




FIG. Z 



Tools of the Chartographer 77 

The illustration on the preceding page shows 
some of the uses to which the Triangle is put when 
operated in connection with its running-mate, the 
T-Square. Triangles are obtainable in numerous 
sizes and angles, the standard angles being 45 
degrees and 30 by 60, the latter commonly called 
"Thirty" by draftsmen. 

THE ENGINEER'S SCALE 

Important uses will also be found in chart 
making for the engineer's rule or scale. It is an 
equilateral triangle in shape, that is, all its sides 
are equal; it is usually made of hardwood, 12 
inches in length (although different lengths are 
procurable), and has three edges each with two 
measuring surfaces. These six surfaces are laid 
off into multiples of 10, with 10, 20, 30, 40, 50, and 
60 units to the inch, and in consequence they 
provide measurements of almost any fraction of 
an inch that can be quickly applied to varying 
scale units of less than an inch. The engineer's 
scale is admirably adapted to linear measure- 
ments, that is, to measurements pertaining to or 
of the nature of a line or in one direction. 

The engineer's triangular scale is not to be 
confused with the architect's triangular scale, the 
latter having the inch divided into units of fourths, 
eighths, sixteenths, thirty-seconds, and so on, 



78 Chartography in Ten Lessons 

and which is of little use to the chartographer. 
The student is cautioned against making use of 
the engineer's rule for ordinary ruling purposes, 
as this use wears away the ruled edges and in 
time makes ineligible the sub-divisions of the 
inch. 

THE DIVIDERS 

Assistance in the drawing of a chart is also 
rendered by the use of the compass or dividers. 
It consists of a handle from which extends two 
prongs each having a sharp point. In the handle 
is a joint, either a pivot or tongue, which permits 
adjustments between the two points up to several 
inches. This enables the draftsman to "step- 
off" or gauge accurately any measurements on 
lines or charts that are to be transferred to other 
lines or charts. Greater accuracy will be se- 
cured from the use of the dividers than from that 
of the ordinary ruler for this purpose. 

Every draftsman has use for kneaded rubber, 
art gum, and the "ruby" or red rubber eraser for 
erasure purposes. A hard rubber or gritty eraser, 
such as the ordinary typewriter eraser, should 
not be used. A supply of pins, clips, thumb 
tacks, and the like will also come in handy. 

THE ESSENTIAL TOOLS 

The following summarizes the more important 
tools needed in chartography : 



Tools of the Chartographer 79 

One drawing pencil HB. 

One ruling pen. 

Six Gillett's No. 303 and six Easterbrook's 
No. 14 pen points. 

One bow or compass pen with interchangeable 
pen and pencil points and extension bar. 

One bottle Higgin's waterproof black drawing 
ink. 

One drawing board or table. 

One T-Square. 

One six-inch celluloid 45 degree triangle. 

One twelve-inch engineer's triangular rule. 

One dividers. 

These tools can each be bought separately but 
a material saving is made by purchasing a com- 
plete set of drawing instruments at the outset. 
The price naturally varies according to the quality 
but an expensive set is not necessary for good 
work. The outfit of the chartographer may be 
simple or elaborate according to individual taste. 
A few well selected instruments of standard make 
is recommended at first. Where the beginner 
confines himself to a limited number of tools he 
becomes familiar with the "feel" and balance 
of each instrument and, as a result, soon learns 
to handle it with confidence and skill. This 
applies especially to the drafting or ruling pen. 



QUESTIONS FOR SELF-EXAMINATION 

1. What is cross section or coordinate paper? What ser- 
vice does it perform in chartography? 

2. What is the function of the lead pencil in chart 
making? 

3. What is the ruling pen? Describe the correct posi- 
tion for holding it. What is a "shoulder" and what causes 
it? How can it be prevented? |f| % . ^ fe^g 

4. Describe the drawing board and its uses. 8 |# 1 

5. What is the T-Square and what are its uses?^ The 
Triangle? 

6. What is the engineer's scale? How and for what 
purposes is it employed? - > A p :. - ||| ^ t ;• 

7. Describe the dividers and its uses. ^ \ -V 

8. What are the essential tools in chartography? 



80 



CARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON VII 

ACCURACY IN 
CHARTOGRAPHY 



Copyright, 1919, by F. J. Wmnt 
PUBLISHED BY 

FRANKJ.WARNE 

SOUTHERN BUILDING 

WASHINGTON. D.C. 




NOV -7 19F9 



DCi.A5.'i(54' 



w> 



\\fo\ 






^t% 



LESSON VII 

Accuracy in Chartography 

The Use of the Typewriter — Drawing Letters 
for the Title — Exaggerating the Curve — Effects 
of Exaggerating the Curve — Advantages of 
Extra Squares. 

In placing on the chart the figures of the scale 
lines, the statistical table, the foot-notes, and 
other figures and letters the use of the typewriter 
enables the chartographer to meet many of the 
exactions encountered in the practice of his art. 
This is especially true when a large number of 
different charts has to be made for reproduction 
in quantities by means of one of the photographic 
processes. 

THE USE OF THE TYPEWRITER 

If a long-carriage machine is not available and 
if the coordinate sheet is too large for the ordinary 
typewriter the sheet can be cut in two and after- 
wards pasted together. This makes necessary 
the exercise of care in handling the sheet after- 
wards or else the typewritten figures will "rub." 
This work on the typewriter should be done after 
the lines and curve or bars are completed. 

Another practice that has many advantages is 

81 



82 Chartography in Ten Lessons 

first to typewrite the numbers and words on 
separate slips of paper and then paste these 
securely in their proper places on the section sheet. 
This plan should be followed if the chart is to be 
reproduced. It enables corrections to be made 
more easily and does not wrinkle or otherwise 
damage the sheet. If the chart is not to be 
reproduced, the letters and figures should be 
written according to the first plan, that is directly 
on the coordinate sheet itself. 

Typewriting the table directly on the chart or 
on a separate slip of paper and later pasting this 
on the sheet, requires considerable painstaking 
care. The typed figures and letters must be 
clean, decimal points separating the digits must 
be in column order equally exact with the fig ires 
themselves, units of tens or hundreds and so on 
must be under each other, and all in straight 
columns with headings appropriately placed at 
the top of each. In pasting the slip on the sheet 
exactness is required so as to avoid the appearance 
of "skewness." Corrections can more easily be 
made with the figures and letters on the slip 
than with them directly typed on the coordinate 
sheet. 

In the employment of the typewriter for plac- 
ing words and numbers on a chart that is to be 
reproduced by a photographic process, care must 



Accuracy in Chartography 83 

be exercised in seeing to it that the ink of the type- 
writer ribbon is of a quality that will reproduce. 
I know of the experience of a fellow chartographer 
who had in progress a rush contract for several 
hundred different charts on each of which was 
to be reproduced a statistical table. He failed 
to have proper attention given to overseeing the 
typing of these tables, with the result that not 
one would reproduce because the right kind of ink 
was not used, In itself the kind of ink may be a 
small matter but the consequence of not using the 
right kind is likely to prove serious and costly. 

DRAWING LETTERS FOR THE TITLE 

Virtually all the figures and letters required on 
a chart can be placed in their proper positions 
by means of the typewriter with the exception of 
the title letters. These latter are usually larger 
than those of the typewriter, although even for 
the title the capitals of the typewriter can some- 
times be made to serve the requirements. As a 
general thing, however, the use of the typewriter 
for the title letters is inadvisable. 

It is this lettering for the title that is among 
the exactions of chartography with which the 
beginner is likely to have some difficulty. He 
mu^st learn how to make the kind of letters 
required. This is not so difficult as might at 



84 



Chartography in Ten Lessons 



first appear; in fact it is quite simple, and by a 
little practice the student can soon become pro- 
ficient in this phase of the work. 

In making these larger letters the minute 
squares of the coordinate sheet are of material 
assistance. After determining upon the size of 
the letter required, the horizontal and vertical 
lines of each letter are drawn by the ruling pen 
and with the aid of the minute squares. The 
curved corners are first left blank, as illustrated 
in the following : 



ins 



Then the curved corners are filled in with a free 
hand pen. 

For the guidance of the beginner in chartog- 
raphy the letters of the alphabet are reproduced 
on the opposite page as samples of plain and 
easily made letters based upon the above instruc- 
tions as to how they are to be drawn. No 
attempt is made to present other than a simple 
utility alphabet, all the letters with the exception 



86 Chartography in Ten Lessons 

of I, M, and W being approximately of the 
same width. Illustration is also given as to the 
drawing of large figures. 

EXAGGERATING THE CURVE 

The beginner in chartography, however, should 
know how to make letters and should not neglect 
to become proficient in this direction. Practice 
in lettering teaches painstaking accuracy-, and 
this is demanded of the good chartographer. 
In chart making he will have many opportunities 
for acquiring this personal asset. 

Especially is this true in the process of determin- 
ing and plotting the scales for the curve chart. 
He must be certain that his vertical scale does 
not permit of the exaggeration of the movement 
of the curve. This exaggeration easily results 
in not allowing for the vertical scale the same 
amount of space per each scale unit as for the 
horizontal scale, and vice versa. In other words 
the movement of the curve can be exaggerated 
either vertically or horizontally. 

"The scales of any curve chart should be so 
selected," says Brinton, in Graphic Methods for 
Presenting Facts, "that the chart will not be 
exaggerated in either the horizontal or the ver- 
tical direction. It is possible to cause a visual 
exaggeration of data by carelessly or intentionally 



Accuracy in Chartography 87 

selecting a scale which unduly stretches the chart 
in either the horizontal or the vertical direction." 

"The beginner in curve plotting and in curve 
reading/' continues Brinton, "is apt to be 
somewhat puzzled by the different effects which 
may be obtained by changing the ratio between 
the vertical scale and the horizontal scale. It 
is difficult to give any general rules which would 
assist in overcoming the beginner's confusion. 
Ordinarily the best way to get facility in making 
the proper choice of vertical and horizontal 
scales for plotting curves is to take one set of 
data and plot those data in several different ways, 
noticing the changes which the different scales 
selected give in the proportions of the chart. 
Just as the written or spoken English language 
may be used to make gross exaggerations, so 
charts and especially curves may convey exag- 
gerations unless the person preparing the charts 
uses as much care as he would ordinarily use to 
avoid exaggerations if presenting his material 
by written or spoken words." 

"A person reading charts must take great 
care," concludes Brinton on this point, "that 
he does not give too much weight to the actual 
appearance of the curve on the page, instead of 
basing his conclusions on the percentage increase 
or decrease as judged from the figures of the ver- 



88 Chartography in Ten Lessons 

tical scale. The proper choice of scales for curve 
plotting is largely a matter of judgment, and the 
judgment can be trained very greatly if it is kept 
in mind to examine every curve chart which 
comes to one's attention to see whether the verti- 
cal and horizontal scales have been selected so that 
the chart gives a fair representation of the facts." 

EFFECTS OF EXAGGERATING THE CURVE 

The effects of an exaggeration of the vertical 
scale can be seen from a study of the chart on the 
opposite page. The units of the vertical scale 
are there purposely made twice the distance apart 
than are units of the horizontal scale. The result 
is an exaggeration to the eye, in the rise and fall 
in the movements of the curve across the sheet, 
of just twice what these movements should be. 

In order that the student may comprehend 
clearly for himself just what this exaggeration of 
the curve means, it is suggested that he draw on 
the chart on page 89 in light lead pencil a broken 
or dash curve that conforms to a scale by which 
the distance between the horizontal lines is re- 
duced one-half. In other words, he is to give to 
each horizontal and vertical scale unit exactly 
the same space. 

Rearranging the vertical scale units accordingly 
the unit 7 falls on the vertical line at a point half 



IMMIGRATION TO UNITED STATES BY MONTHS. 1918 



Thousands off Immigrants 
Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. ffor. Deo. 



i.6 










\ 


















15 
14 
13 
















\ 






Jan. 6,356 
Feb. 7,388 
Mar. 6,510 
Apr. 9,541 
May 15.217 
June 14,247 
July 7,780 
Aug. 7,862 
Sept. 9,997 
Oot. 11,771 
Nov. 8,499 
Dee. 10,748 


- 






































12 
U 
10 
9 
8 






























/ 






















/ 




/ 






j 
















/ 




















\ 


/ 


/ 


\ 




















A 


/ 


\ 


J 



















Statistics are from Bureau off Imnigrat Ion 
0. 3. Department off Labor 



90 Chartography in Ten Lessons 

way between the unit 6 and the present 7, and the 
point now marked by the latter becomes the 
place for the scale unit 8. Proceeding upward 
in this manner cross out with the lead pencil each 
of the old vertical scale units and substitute the 
new units according to the revised plotting. Re- 
produce in lead pencil this new scale also alongside 
the extreme right vertical line. Connect these 
new left and right vertical scale points by horizon- 
tal lines in light lead pencil. Next draw the 
curve from point to point of the vertical lines as 
determined by the revised units. 

It will now be found that this new curve moves 
up and down exactly one-half the distance of the 
original curve. The new curve starts at a 
point on the left vertical line just above the pre- 
sent scale designation 6 and ends at a point on the 
right vertical line half way between the present 
scale units 8 and 9. These vertical scale units 
represent thousands of immigrants, as explained 
in the word designation just above the horizontal 
scale line. 

It is important to remember in connection with 
the exaggeration of the curve that the arbitrary 
limitations of space imposed upon the chartog- 
rapher does not permit him in every case to choose 
the scale that might have been chosen if there 
were no factors to consider other than the exact 



Accuracy in Chartography 91 

presentation of the statistics. His problem is to 
present the facts as clearly as possible within the 
arbitrary limitations of space imposed upon him. 
Sometimes he will find himself in a quandary in 
his endeavors to include all the necessary data 
without exaggerating one or the other of the 
scales. 

ADVANTAGES OF EXTRA SQUARES 

Reducing by one-half the space allowed the ver- 
tical scale unit in the chart on page 89 brings the 
lowest and the highest points of the curve within 
a space of less than three inches, thus decreasing 
horizontally as compared with the old curve the 
size of the area within which the curve moves 
without affecting its size vertically. Plotted in 
this way results in an awkward size for the chart. 

This can be overcome by providing at least two 
series of squares both below the lowest and above 
the highest points recorded by the movement of 
the curve. In such cases the vertical and hori- 
zontal lines forming the squares are drawn just as 
if they were to be used to indicate a stage in the 
movement of the curve. This extension of the 
area of the squares should also be regulated so as 
to accommodate the placing of the statistical 
table without crowding. It will nearly always be 
found feasible in plotting the vertical scale to 



92 Chartography in Ten Lessons 

provide for at least one series of squares vertically 
into which the movements of the curve do not 
enter. This will be found to be advantageous in 
a number of ways. It adds to clearness of expres- 
sion as well as avoids the appearance of crowding. 
If the exaggeration of the scale in the chart on 
page 89 had been in the horizontal instead of the 
vertical measurement, just the opposite effects to 
those noted would have resulted. It is suggested 
that the student draw a chart in which he gives 
twice the space to the horizontal scale unit that he 
gives to the vertical scale unit, using the data in 
the statistical table of the chart on page 89. 

QUESTIONS FOR SELF-EXAMINATION 

1. Describe the various uses of the typewriter in chart- 
ography. 

2. How are large letters drawn by hand? 

3. How is the curve exaggerated? What are some of its 
effects? How can these be avoided? 

4. What are the advantages of extra squares? 



CHARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON VIII 

CURVE AND BAR 
DESIGNATIONS 

Copyright, 1919, by P. J. Warne 



PUBLISHED BY 

FRANK J. WARNE 

SOUTHERN BUILDING 
WASHINGTON, D.C. 



KM 



n 





NOV -7 1919 

©CLA5364 



HA*i 






^m 



LESSON VIII 

Curve and Bar Designations 

Disadvantages of the Unbroken Curve — Curve 
Designations — Word Designations of Curves — 
The Peak-Top Curve — Determining the Scale 
Spacing — Utility of the Curve Chart — Chartog- 
raphy Based on Comparisons — Bar Designa- 
tions — Interpreting the Bar — Some Character- 
istics of a Good Bar CharU — Word Designation 
of Scale Units. 

It is plain that if a number of curves on the 
same chart are each drawn as an unbroken curve 
much confusion will accompany efforts to interpret 
the tendencies shown, as most likely the curves 
cross and re-cross each other. This is illustrated 
in the chart on the following page. 

disadvantages of the unbroken curve 

Let the student try to follow each curve from 
its beginning on the left vertical scale line to its 
termination on the right vertical scale line. It 
is hardly possible that he accomplishes the task 
successfully in every case by ending on the curve 
he starts out upon, as indicated by the initial 
abbreviation of the name of the railroad. Even 
if he does succeed he will have spent a great deal 

98 



»* -* m < 







Curve and Bar Designations 95 

more time than should be required to interpret 
such a chart correctly. Among the aims of 
chartography is to prevent confusion and to aid 
comprehension at a glance, and the reading of a 
chart should not have placed in the way obstacles 
like those illustrated on the opposite page, es- 
pecially when the obstacles have no reason or 
even excuse for being. A study of the chart 
should quickly convince the student of the dis- 
advantage of using the same kind of unbroken 
curve for two or more statistical elements on the 
same chart. Reading the chart in question is 
only slightly aided by placing at the left and right 
vertical scale lines the abbreviations of the names 
of the different railroads which the curves 
represent. 

CURVE DESIGNATIONS 

Attention is thus called to a practical condi- 
tion confronting the chartographer which would 
be replete with difficulties did he not have re- 
course to a simple device to overcome them. 
This is the employment of different designations 
for two and more curves. 

In contrast with the unbroken or straight line 
curves of the chart on page 94, those of the chart 
on page 96 should be studied. The latter com- 
pare as many as nine separate and distinct sta- 



AVERAGE PRICES*OF MEAT PRODUCTS 

UNITED STATES. I 913 — 1819 



Cents 
1916 



1913 1914 1915 1916 1917 1918 1919 

Bacon 26.7 26.7 26.4 28.1 38.2 49. S 57. 2 

Haa 26.5 26.8 25.3 31.2 36.5 44.6 52.9 

Sirloin Steak 26. 4 25.4 25.1 27.0 31.7 36.6 43.7 

Bound Steak 22.3 23.0 22.5 24.0 28.9 34.5 40.5 

21.6 21.6 19.7 22.5 30.6 35.6 41.4 

20.2 19.3 21.0 23.0 27.6 35.3 39.9 

19.9 20.1 19.* 21.0 25.2 29.3 34.6 

16.2 17,0 16.0 21.2 21.2 25.5 29.4 

12.2 12.4 12.2 12.8 16.1 19.9 22.6 



Pork Chope 

Lanfc 

Rib BbaaV 

Chuck Roast 

Plate Beef 



Round Steak. 

P«* Chops 



Chuck Roast 




Curve and Bar Designations 97 

tistical elements, presenting two more curves 
than are in the chart on page 94, and yet there is 
not the slightest difficulty or confusion in tracing 
the nine curves from their beginning to their 
termination. This greater clearness and ease of 
interpretation is almost entirely due to the fact 
that a different designation is given to each curve. 
If this had not been done it would be almost as 
difficult to follow the curves in the chart on page 
96 as in the chart oh page 94 — the curves of the 
former would also be lost, as to the reading of 
their movement, at the points where they cross 
and re-cross one another. 

Quite frequently the student of chartography 
will encounter the problem of having many 
curves to compare. While this difficulty is met 
in part by employing different designations for 
the curves, there will be occasions when even 
this method will result in confusion. Under such 
circumstances, instead of attempting to draw all 
the curves on a single chart, it will be found 
advantageous to make two or more charts. One 
set of the group of figures should be selected as a 
common basis for the comparison and the curve 
representing this set or statistical element in- 
serted on all the charts, this curve taking the 
same unbroken or straight line designation on 
each chart. It is a mistake to place a larger 



98 Chartography in Ten Lessons 

number of curves on one chart than can be read 
quickly and without confusion to the eye in 
tracing their movements. Where the curves lie 
close together or are constantly crossing and re- 
crossing each other, more than five or six are 
likely to result in this confusion. 

It is in making clear just such problems as 
those presented in the chart on page 96, where a 
number of different statistical elements must be 
compared, that the advantage of the curve method 
over the statistical method becomes apparent. 
To grasp quickly and comprehendingly the mean- 
ing of each of the nine different columns of figures, 
not only in relation to its own element over the 
period of years but also in relation to each of the 
elements of the other eight columns, is prac- 
tically an impossibility to most minds. And 
yet one of average intelligence can easily read 
the trend or tendency of these prices of different 
kinds of meats when interpreted by the curves. 

WORD DESIGNATIONS OF CURVES 

Not only from the point of view of interpretation 
but also of mechanical construction the chart on 
page 96 is recommended for close study. Note 
the word designations of the curves to the left 
and right of the vertical scale lines. This inser- 
tion of the word designation alongside the point 



Curve and Bar Designations 99 

of contact of the curve with the vertical scale 
lines lends to easy reading of the chart. It 
requires, however, extending the space between 
each vertical scale line and its respective neat 
line, and this is not always possible. In such 
cases the curve designations with their word 
descriptions should be placed at some convenient 
place on the framework itself as a sort of key or 
legend. Quite frequently a good place for the 
legend will be found to be just beneath the bottom 
horizontal line and above or between the foot- 
notes. 

The different designations that can be em- 
ployed for curves should be practiced by the 
student until he has acquired facility in drawing 
them. To assist him in this the following page 
of designations is presented. These have been 
made considerably larger than is necessary for 
the curve on the chart. 

THE PEAK-TOP CURVE 

I The student is cautioned against making use of 
what is called the "stairway " curve. This makes a 
flat or step-like contact at the point determined by 
the scale. All curves, as has been said, should 
approach the point of contact slantingly and 
direct from the point previously touched on the 
vertical line. The great advantage of this 



Curve and Bar Designations 101 

peak-top curve is brought out on charts contain- 
ing two or more curves which approach each other 
at or near the same points. In such cases the peak- 
top permits of easy separation of the two curves 
and does not result in confusion caused by in- 
ability to follow the curves, which latter is inevit- 
able when two flat-top or stairway curves ap- 
proach each other at the scale unit points. 

DETERMINING THE SCALE SPACING 

In determining the vertical space a number of 
curves should occupy every one of the columns of 
figures in the statistical table is examined to ascer- 
tain the lowest and highest numbers that are to 
be charted. That is, for this purpose all the differ- 
ent columns representing the comparable statis- 
tical elements are considered as if they were only a 
single column. 

Take, for illustration, the table of the chart on 
page 96. The lowest number of cents represented 
in any one of all seven columns is 12.2 in the col- 
umn for the year 1913. This number also appears 
in the column for the year 1915. The largest 
number of cents in any one of all the columns is 
57.2 in the column for the year 1919. Thus the 
spread for all the numbers in all the columns is 
from 12.2, the price of plate beef in 1913 (also in 
1915), to 57.2, the price of bacon in 1919, or a max- 



102 Chartography in Ten Lessons 

imum spread for all the figures of 45. With a verti- 
cal scale unit of 5 this spread requires at least ten 
squares vertically with the base line starting at the 
unit 10. Starting at would require two addi- 
tional squares below the scale unit 10, but if this 
were done there would not be space enough any- 
where on the framework for the inclusion of the 
statistical table. Our squares are thus more 
valuable at the top, so we provide two additional 
there to accommodate the table. 

UTILITY OF THE CURVE CHART 

By this time the student should have become 
impressed with the great utility of the curve 
method in chartography. In comparing the 
tendency over a period of time of two or more dis- 
tinct but related statistical elements it is far 
superior to the bar method in chart making and 
incidentally is also superior to the statistical me- 
thod. While a trained statistician could interpret 
satisfactorily the tendency from a study of col- 
umns of figures, no one else could perceive the 
movement as clearly as it is convincingly demon- 
strated by curves drawn in relation to each other. 

This is particularly true when more than two 
curves representing different columns of figures are 
compared, as in the chart on page 96. These 
curves not only show the variations in each of the 



Curve and Bar Designations 103 

items for each year compared with the other years 
and with the other items but they also give a 
comprehensive perspective of the entire movement 
during all the years; they show the status of 
each of the items in relation to every other item 
for each year and at the beginning and through 
to the end of the period of time. Thus it is that 
chartography can be said to "speak" a language 
easily made intelligible to the mind through the 
eye. 

CHARTOGRAPHY BASED ON COMPARISONS 

The curve also strikingly emphasizes the fact 
that the art of chartography is based upon rela- 
tions or comparisons. There can be no chart 
without a comparison of some kind. And as the 
very nature of statistics involves a relation be- 
tween or a comparison of groups of facts, it is 
hot too much to say that chartography is the art 
best adapted to expressing this clearly and con- 
cisely. 

"Comparison is, in general, the final goal to- 
ward which all statistical studies tend," says King, 
in his Elements of Statistical Method. "Com- 
parison is necessary to give us clear ideas of the 
relationship of things in time and space. It is also 
essential in determining whether phenomena are 
connected or independent and in establishing 
relations of cause and effect. Wefmay wish to 



104 Chartography in Ten Lessons 

study: 1. Changes of a single variable. 2. The 
structure of different groups. 3. Changes in two or 
more variables." 

Brinton, in his Graphic Methods for Presenting 
Facts, puts it this way: "One of a business man's 
chief assets is his ability to show things to others 
in their true proportions. He is continually mak- 
ing contrasts, and holding up for comparison 
different propositions which come up in his daily 
affairs. The graphic method lends itself admir- 
ably to use in making comparisons. It is surpris- 
ing how much clearer even simple comparisons of 
only two or three items will appear when their 
numerical value is put in graphic form rather 
than in figures." 

In every chart, then, a comparison or relation of 
some kind is involved. This comparison may be 
with the same statistical element for two or more 
periods of time; it may be of two or more differ- 
ent elements for the same or different periods of 
time. It may be a comparison of total or abso- 
lute amounts, of increases or decreases, of the rate 
of change. It may be a relation of one or more 
elements expressed in proportions to a common 
total, and so on. 

Graphic methods must, of course, show compar- 
able facts only and these in their true relations 
and proportions in order to present the correct sit- 



Curve and Bar Designations 105 

uation. They represent the best known scheme 
for presenting contrasts and in this way indelibly 
impressing their significance upon the mind. Hav- 
ing recourse to curves differently constructed 
permits some of these comparisons to be made 
much more clearly than if the chartographer 
were limited to the unbroken or straight line 
curve. 

BAR DESIGNATIONS 

Different designations for different statistical 
elements or factors apply with equal significance 
to the bar as to the curve chart. The simplest 
designations are plain black and white which are 
usually employed where only two groups of 
figures or statistical elements are involved. The 
plain white bar is secured simply by outlining it 
on the section sheet and without filling it in with 
the ink. But it is not as satisfactory as a cross- 
hatched bar, that is, one with the outline filled 
in by drawing light diagonal lines. 

One use of designations in bar charts is illus- 
trated in the chart on page 106. The student 
should write out on paper a careful analysis of 
this chart, not only from the point of view of its 
construction but also from that of interpretation. 

Another and probably the most common use 
of designations in bar charts is illustrated on 
page 107. It shows the employment of the black 



OPERATING REVENUES AND EXPENSES 

PENNSYLVANIA RAILROAD 
Billions of Dollars 




Operating Expense* 



Conpiled f roa Reports of Railroad 
to Interstate Caanerce Coamission 



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108 Chartography in Ten Lessons 

and white as parts of a whole bar. In this chart 
the total freight traffic of the Norfolk and Western 
Railroad Company has been separated on the 
percentage basis between bituminous coal and 
all other commodities transported. The com- 
parison involved is expressed as a ratio. The 
changes over the period of years of the coal 
traffic in relation to the total traffic, as well as 
also in relation to the traffic in all other com- 
modities, is seen by comparing the black portions 
of the bars with the total bars, reading from left 
to right. Similar changes in the proportion of 
the traffic of other commodities to the total 
freight traffic is shown by comparing the white 
portions of the bars with the total bars, reading 
from right to left in order better to secure an 
idea of the differences in the length of the white 
sections. The proportion of each designation 
to the total bar in any one year and the changes 
as between years are clearly indicated. 

In this chart each of the series of horizontal 
bars represents by 100 per cent the total amount 
of all freight traffic for each of the designated 
years. Consequently all the bars are of the same 
length. No information is given as to the 
numbers representing the absolute amount of 
traffic of the road, which it may naturally be 
assumed varied in the different years — it may 



Curve and Bar Designations 109 

have increased or decreased from year to year 
and if these numbers were charted they would 
likely give bars of varying lengths. All that the 
chartographer is interested in, so far as the sta- 
tistics enlighten him, are the changes in the pro- 
portion of the two components which together 
comprise the total freight traffic for each year. 

SOME CHARACTERISTICS OF A GOOD BAR CHART 

The chart on page 107 is a good illustration of 
this kind of a bar chart. The title is concise and 
yet comprehensive. The sub-title — that of the 
particular railroad — is well placed and well 
spaced. The figures for the years are directly 
under each other and are spaced sufficiently from 
the bars, while the figures for the black and white 
portions of the bars are directly in proper column 
form on each of the six bars. The reader is told 
at the top of the framework that the figures 
represent per cents, and at the bottom among the 
foot-notes that the statistics have been "Com- 
piled from Reports of the Railroad to Interstate 
Commerce Commission." The group of bars is 
so spaced as to avoid the appearance of crowding. 
The designations of the bars are clearly distin- 
guished between "Bituminous Coal" and "Other 
Commodities" by means of the legend beneath 
the bars. The neat lines properly frame the 
series of bars. 



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Curve and Bar Designations 111 

When more than two statistical elements have 
to be indicated on a bar the chartographer has 
recourse to an almost unlimited number of differ- 
ent designations. Some of these, shown in the 
chart on the opposite page, indicate the extent 
to which variation in bar designations can be 
carried. The effect of the use of these different 
designations is for the purpose, of course, of 
causing the areas to stand out in contrast with 
each other. The student should practice until 
he becomes proficient in making these designa- 
tions. 

In the chart on page 89 (Lesson VII) and in the 
one on page 106 will be found a simple device and 
yet a valuable aid to chartography. This is the 
word designation of the vertical scale unit of a 
curve and the horizontal scale unit of a bar chart. 

In the chart on page 89 (Lesson VII) this 
designation is "Thousands of Immigrants." By 
its use the chartographer is able to drop from each 
of the vertical scale units all the ciphers repre- 
senting thousands. That is, instead of the vertical 
scale starting with the unit 6,000 it begins with 6, 
the interpreter of the chart knowing from having 
read the word designation that this unit 6 means 
6,000. So with the horizontal scale unit of the 
chart on page 106. There the word designation is 
4 'Millions of Dollars" and this permits the drop- 



112 Chartography in Ten Lessons 

ping of six ciphers from each of the horizontal 
scale units— it allows the scale to begin with 
the unit 100 instead of requiring 100,000,000. 
To reproduce the additional six ciphers after each 
one of the horizontal scale units would over- 
burden the horizontal scale line with figures even 
if space could be found for all of them. 

Making use of the word designation of the 
scale so as to drop the ciphers from the scale line 
itself has many advantages and should always be 
employed where the numbers represented are 
more than three digits, that is, thousands and 
over. The designation should be clearly pre- 
sented in an easily observable place on the chart, 
even when the table of figures would seem to 
make this unnecessary, so that the chart can be 
quickly read and easily understood without 
reference to the statistics from which it is made. 
Usually the best position for the word designation 
is just beneath the top neat line and centered 
above the horizontal scale line. 

QUESTIONS FOR SELF-EXAMINATION 

1. What are the advantages of various designations for 
different curves? 

2. Describe the peak- top curve. 

3. How is the scale spacing determined? 

4. Describe the utility of a curve chart. 

5. What is the basis of chartography? 

6. Discuss the uses of various designations for different 
bars. 



CHARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON IX 

STATISTICS AND 
CHARTOGRAPHY 

Copyright, 1919, by P. J. Warns 



PUBLISHED BY 

FRANKJ.WARNE 

SOUTHERN BUILDING 
WASHINGTON. D.C. 



e-o^-j, ^. 



-7 1919 



).Ct,A53e47 



tJA31 



LESSON IX 

Value of Statistics to Chartography 

The Statistical Table — Aids in Reading the 
Table — The Substitution of Ciphers — The 
Table of Ratios — Building Up A Table — The 
Percentage Increase and Decrease — The Zero 
Line — The Arithmetic Average — The Misuse 
of the Average — Statistical Class Limits. 

It should be clear by this time that a most 
important asset in the practice of chartography 
is a knowledge of statistics. The mere mechani- 
cal act of drawing lines and curves and bars on 
section paper is the work of the draftsman and 
does not of itself make a chartographer. In 
these Lessons it has been assumed that the infor- 
mation is already at hand in proper form for the 
drawing of the chart — that the collection and 
compilation of the statistics have been correctly 
done and that the figures have been checked 
and verified so that there is no question as to their 
accuracy and trustworthiness. 

This assumption has been necessary for the 
reason that statistics are a distinct field of study in 
themselves, with sub-divisions as to methods of 
collection, of compilation, of tabulation, of compu- 
tation, of arrangement, of presentation, of inter- 

113 



114 Chartography in Ten Lessons 

pretation, and so on. This field is entirely too 
extensive to be presented in these Lessons even 
in merest outline, and for a knowledge of its 
principles the student should have recourse to 
standard books on the subject. All that can be 
done here is to make the briefest reference to a few 
only of its features which most vitally concern 
the beginner in chartography. 

THE STATISTICAL TABLE 

Conspicuous among these is the arrangement of 
the statistical elements in the table. The prin- 
ciples underlying this have necessarily been dis- 
cussed briefly in preceding Lessons. But there 
is one other point in particular to which attention 
must be called. This is the more or less common 
practice — fortunately it is becoming less common 
as the rules of good chartography become more 
widely disseminated and better known — for 
charts to appear in otherwise first-class publica- 
tions with the statistical table having the latest 
date at the top and with the earliest period of time 
at the bottom of the column. 

A chart made from a table arranged in this 
way reads backwards from the latest to the 
earliest year. In order to interpret it from the 
earliest year and in sequence of time it has to be 
read from right to left, which is the wrong way to 



Value of Statistics to Chartography 115 

read a chart. Invariably this arrangement is at 
first glance misread, as the natural inclination of 
the reader is to assume that years are arranged 
in proper sequence. Where they are not so ar- 
ranged too much time is lost before this is realized. 
The first impression on the interpreter of the 
chart in such cases is exactly the reverse of that 
intended and which would have been received 
by him if the correct method of arranging the 
statistical elements in table form had been fol- 
lowed. In consequence, one of the fundamental 
purposes of the chart method of disseminating 
knowledge is violated. Such a practice should 
not be indulged in even in exceptional cases. 

RECONSTRUCTING THE TABLE 

Whenever the chartographer has a table of 
figures to chart in which the latest year or period 
of time appears at the top of the column, he should 
rearrange or reconstruct the table in correct col- 
umn form with the earliest year at the top before 
he begins planning his chart. 

The justification for presenting the latest year 
first in the column is that it is of greater impor- 
tance compared with the other years recorded. 
As a matter of fact, no one year in a series of years 
that charts a tendency is of any greater impor- 
tance than the other years. It may be of greater 



116 Chartography in Ten Lessons 

importance in the mind of some particular indi- 
vidual or individuals as to the significance of the 
data it discloses but in itself as a year it is only of 
equal importance with every other year. Besides, 
chartography offers other and much better 
methods for placing emphasis on particular statis- 
tical elements. 

AIDS IN READING THE TABLE 

It may be advisable, where large numbers are 
the basis of a chart, to substitute ciphers as the 
last two figures in tens of thousands, the last 
three in hundreds of thousands, and the last five 
in millions. By raising or lowering the last 
preceding digit before the cipher, sufficient 
accuracy is obtained for the purpose of most 
charts. The advantage of this is that the ciphers 
enable the mind to grasp more quickly the signifi- 
cance of the numbers. In financial statements, 
however, this practice has objections. 

Necessary space on the chart for the columns of 
figures can sometimes be secured by dropping 
entirely the last three or six digits and substituting 
at the head of the columns a word description of 
the amount represented, such as thousands or 
millions and so on as the case may be. This elimi- 
nates the confusion to the eye of numerous digits. 
While this practice is not only admissible but 
also advisable in designations of the scales it should 



Value of Statistics to Chartography 117 

not be allowed to become general in tabulations, 
not even where the value or volume or quantity is 
so large as to run into seven or more digits, as long 
as there is space on the chart to show the complete 
numbers without crowding. 

Assistance in the direction of facilitating the 
rapid reading of a statistical table and in enabling 
a quicker grasp of its significance, is rendered in 
cases of long columns of figures by breaking up 
the numbers into groups of fives with double the 
space separating each group. For illustration, 
instead of presenting the table on the chart like 
this: 

Year Population 

1900 75,994,575 

1901 77,747,402 

1902 79,365,396 

1903 80,983,390 

1904 82,601,384 

1905 84,219,378 

1906 85,837,372 

1907 87,455,366 

1908 89,073,360 

1909 90,691,354 

1910 92,309,348 

1911 93,927,342 

1912 95,545,336 

1913 97,163,330 

1914 98,781,324 

1915 100,399,318 

1916 102,017,312 



118 Chartography in Ten Lessons 

It might better be presented as follows: 

Year Population 

1900 76,000,000 

1901 77,700,000 

1902 79,400,000 

1903 81,000,000 

1904 82,600,000 

1905 84,200,000 

1906 85,800,000 

1907 87,500,000 

1908 89,100,000 

1909 90,700,000 

1910 92,300,000 

1911 93,900,000 

1912 95,500,000 

1913 97,200,000 

1914 98,800,000 

1915 100,400,000 

1916 102,000,000 

These figures represent the population of 
continental United States as reported by the 
Bureau of the Census of the United States Govern- 
ment in its bulletin on mortality statistics for 
1916. Using them as a basis, the student is 
instructed to draw with a lead pencil a curve or 
bar chart, whichever he determines, applying to 
his task the instructions he has received up to this 
point. 



Value of Statistics to Chartography 119 

the substitution of ciphers 
This substitution of ciphers for other digits in 
large numbers does not affect the accuracy of the 
chart for the reason that the change made by it 
in any number is so slight, compared with its 
total, as to be lost in the results of the applica- 
tion of the scale unit to its measurement. Be- 
sides, it has a distinct advantage in that it does 
not accord to the statistics any greater import- 
ance than the method of their compilation war- 
rants. No one who is familiar with the methods 
of taking or enumerating the decennial census of 
the population of the United States and of esti- 
mating its growth for intermediate years believes 
for a single moment that this population, say, in 
1916, was exactly 102,017,312 to the last digit of 
accuracy. While no criticsm of these methods is 
here intended, it is but stating the fact that they 
are not so perfect as to record to the last figure 
the exact population. Most statistical tables at 
best are approximations and do not represent 
absolutely accurate and indisputable facts to the 
point of minute measurement. 

All that can be expected of chartography is that 
it indicate clearly the general trend or tendency of 
statistical elements. The chartographer should 
be on his guard against permitting the curve or 
bar to convey an impression of a greater degree of 



120 CH AUTOGRAPHY IN TEN LESSONS 

accuracy than is warranted by the statistical 
information. 

THE TABLE OF RATIOS 

In dealing with tables of ratios it is always 
advantageous to carry the digits at least one place 
beyond the decimal point. The advisability of 
this should be so clear as not to need to be dis- 
cussed. If, for instance, by not including the 
last digit of the two ratios 67.6 and 32.4 of the 
1912 bar in the chart on page 107 (Lesson VIII) 
each portion of the whole bar falls short of its 
correct measurement and the total 100 per cent 
bar is incomplete. It is hardly ever necessary 
to carry the digits further than two decimals and 
in most cases one digit beyond the decimal point 
answers all practical purposes. 

Frequently decimals exceeding one-half may 
be raised to a whole number and under one-half 
lowered to a cipher. Where the digit is exactly 
one-half whether it is raised or lowered will 
depend upon the particular circumstances. Per- 
centages or ratios are a problem in mathematics 
and it is to that science the student should have 
recourse for more complete knowledge of the 
principles involved. 

As percentages or ratios are derivative figures 
it is of advantage, if it does not over burden 
the chart, to place also on the framework the 



Value of Statistics to Chartography 121 

original figures from which they are derived. 
Where a choice as to exclusion has to be made it 
should be in favor of the retention on the chart 
of the derivative figures upon which it is based. 

BUILDING UP A TABLE 

Both the original and their derivative figures 
appear in the table of the chart on page 122. 
This chart also illustrates the use of the curve in 
expressing ratio. The problem is to show the 
income of the Pennsylvania Railroad Company 
in relation to its securities, that is, the rate earned 
by the latter for each year from 1909 to 1916, 
both inclusive. The basal information as to 
securities and income was secured from the annual 
reports of the company filed with the Interstate 
Commerce Commission in Washington, D. C. 

The amount of bonds representing funded debt 
and the capital stock were added to ascertain 
the total of all securities for each of the years. 
This gives the second column of figures in the 
table to the chart. In order to ascertain the 
total income that is properly related to these 
securities the amount of interest paid on funded 
debt was added to net corporate income for each 
year, which gives the third column. This in- 
formation enables us to ascertain the rate of 
income each year by dividing the amounts repre- 



RATE OF INCOME ON RAILWAY SECURITIES 







PENNSYLVANIA R, R. 


1« 


>C9 


V 


10 IS 


11 IS 


12 1913 19 


14 19 


18 19 


16 


11 

10 
9 














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3 


Capital 
Tear Obligation! 


Bet Corporate 
Income and Per Capital Bet Corporate Per 
Interest* Cent Stock tnoone Oent 




2 

1 




1909 632,603,66 

1910 705,979,77: 

1911 718,508,27 

1912 714,661,50 

1913 739,019, 22< 

1914 745,106,11 
1916 e25, 601,67 
1916 751,143,374 


) 33,422 
52,297 
45,104 

47,626 

50,412 

45,387 

) 43,618 

k 65,496 


574 5.28 314,606,500 19,954,311 6.34 
500 7.41 412,596,974 40,049,136 9.71 
506 6.28 452,443,935 34,663,023 7.67 
136 6.66 453,677,900 37,503,631 6.26 
511 6.82 495,606,621 40,864,476 6.24 
004 6.17 499,265,700 36,397,775 7.29 
866 5.28 499,203,600 33,245,661 6.66 
r 796 8.72 499,204.700 53,733,439 10.76 




2 

1 








A On Funded Debt 






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£^£S£*oE£- 





Value of Statistics to Chartography 123 

senting capital obligations into the amounts 
representing net corporate income and interest 
for each of the corresponding years. The result 
is the fourth or ratio column of the table. The 
other column of ratios — the seventh of the table 
— is ascertained by dividing the amounts repre- 
senting capital stock into the amounts represent- 
ing net corporate income. 

It should be noted that the only comparison 
made by the two curves of the chart is based 
upon the two columns of ratio figures. It would 
better assist comparison in the statistical table 
if these two columns were placed alongside each 
other, but this cannot be accomplished with 
clearness in reading without making another 
table with the column of years duplicated and 
with awkward headings above each ratio column. 
This latter is due to the words expressing the 
exact meaning of the ratio column taking up a 
great deal more space in width than is occupied 
by the three digits and the decimal point. Thus 
to place adjacent to each other the columns that 
are compared is likely to commit an offense more 
serious than is the value of the advantage to be 
gained. 

THE PERCENTAGE INCREASE OR DECREASE 

Quite a different percentage chart is presented 
on page 124. It shows the rate or per cent of in- 



PRINCIPAL ITEMS OF OPERATING EXPENSES. 1908-1913 



BALTIMORE & OHIO 



•I- 1 ■ ■■-« 1. 




?lguree represent "per cents. 
Increase- or decreets la over 1908. 

1909 1910 1911 1912 1913 




> Buildings, etc. "11.41 42.05 47.46 58.65 127.12 
Locomotives • 6.46 41.78 43.81 50.23 74.72 
Ral la and Ties • 9.57 18.11*12.80 12.98 47.35 
Sages » 9.92 12.43 24.32 22.73 37.30 
Fael *10.93 11.30 19.71 10.74 31.34 
Freight Care '17.19 22.60 14.34 22.53 27.78 

. Roadway and Track "21.12 • 1.34 • 5.63 • 3.05 27.78 

Passenger Care '23.04 * 3.95 * 2.98 5.40 3.98 

'Decrease 


-/- 

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Buildings, etc 

Locomotive a * 
Rails and Ties 
Wages 



— — Fuel 
-x— Freight Cars* 
-«— Roadway and Track 
' — — Passenger Cars * 



T Repairs, renewals, and depreciation 



Value of Statistics to Chartography 125 

crease or decrease. This arithmetical principle is a 
most valuable aid to the chartographer, for without 
it many curve charts that are now possible could 
not be made. This is true in most cases where 
the difference between the numbers to be com- 
pared is considerable, that is, where some are 
large and the others small numbers, as a chart 
of these absolute amounts is impossible owing to 
the requirements of space necessary to indicate 
the "spread" between the highest and the lowest. 
But by resolving these varying amounts into per 
cent increases or decreases, as the figures deter- 
mine arithmetically, statistical elements are 
secured which permit of a common measurement 
and in consequence of a comparison of relative 
movements over a period of years. 

The percentage increase or decrease in our chart 
of each element for each year from 1908 to 1913 is 
based upon the amount for 1908. In consequence 
every curve starts from the same point at zero on 
the 1908 vertical line, because it is plain that 
there could be no increase in 1908 over 1908. As 
the per cent figures for every element show a 
decrease in 1909 over 1908 every curve extends 
downward below the zero line to the respective 
points of contact with the vertical line for 1909. 
For each of the following years the curves 
separate more or less widely according to the 



126 Chartography in Ten Lessons 

tendency as indicated by the figures for the 
different elements. 

Taking the year 1913 for illustration, there is 
an increase over 1908 in every one of the prin- 
cipal operating expense items. It also shows 
that the expense of buildings, fixtures, and so on 
had increased faster relatively than that of steam 
locomotives, or of rails and ties, or of wages, and 
so on; that the expense of passenger cars had 
increased less rapidly than that of any of the 
other items, and that this expense was greater in 
1913 than in 1908. 

THE ZERO LINE 

The chart on page 124 presents also the zero line 
feature of chartography based upon percentage 
increase or decrease figures and not on absolute 
amounts. It is one that the student is likely to 
have frequent occasions to make use of. This line 
is indicated by the cipher designation on the 
vertical scale lines. p- Jj^jj 

The zero line is in reality the base from which 
the curves move up or down as the numbers of 
the statistical table and the scale units determine. 
It practically represents the amounts of each of 
the eight elements in the year 1908 as indicated by 
the line drawn horizontally across the chart, for 
the increase or decrease is "over" that year or 
line. In other words, the movement of the 



Value of Statistics to Chartography 127 

curves for any one and all of the six years in rela- 
tion to the zero line is determined by the rela- 
tion of the amount in each year to the amount in 
1908. Thus the fluctuations in the curves from 
year to year should be read or measured from this 
zero line and not from the slopes of the curves 
themselves. 

Facility in the interpretation of such a chart is 
aided if it is clearly indicated that all the move- 
ments of the curves above the zero line mean 
increases over the base year and below that line 
decreases compared with that year. This is accom- 
plished by inserting the words "Increase" arid 
"Decrease" alongside the vertical scale lines on 
either side of the zero line. This shows clearly that 
the vertical scale reads upward from the zero line 
for increases and downward for decreases. 

Assistance in the clear interpretation of such a 
chart is also rendered by making the zero line 
slightly heavier or wider than the other horizontal 
lines connecting at other units of the vertical 
scale lines and at the same time not as heavy or as 
wide as the curve or curves themselves. This 
wider zero line calls the reader's attention to the 
fact that he must interpret the movements of the 
curves from the zero and not from the lowest or 
base line. 

In cases where the figures to be charted show 



128 Chartography in Ten Lessons 

no decreases and in consequence it is not necessary 
to extend the curves below the zero line, then 
this line becomes also the lowest or base line at the 
bottom of the chart and all the movements of 
the curves are above that line. In such cases it is 
not necessary to employ the terms "Increase" and 
"Decrease" above and below the zero line. Nor 
is it necessary in such cases that the zero line be 
made wider than the other horizontal lines. 

While the chart on page 124 designates with a 
cipher the horizontal line from which the move- 
ments of the curves are measured, as a matter of 
fact this line is not a zero line but a 100 per cent 
line. This is true arithmetically for the reason 
that in reality it represents the total amount of 
each element or item for 1908. These were taken 
as the base from which the figures for each of 
the other years were ascertained. Arithmetic 
exactness requires that this line be designated as 
a 100 and not a line. But in this case chartog- 
raphy takes liberties with arithmetic for the sake 
of securing greater clearness in interpretation. 
Experience has taught that because of the general 
lack of knowledge on the part of many of those 
for whom charts are prepared, confusion leading to 
misinterpretation, and this to misinformation, 
results whenever the 100 per cent designation 
is employed in place of the cipher. 



Value of Statistics to Ch autography 129 

the arithmetic average 
In the chart on page 124 the basis upon which 
the respective percentages have been computed 
is, as has been said, an amount for a single year. 
Wherever possible this basis should be the average 
of the amounts for a number of years, and this is 
nearly always feasible when the number of years in 
the table comprises ten or more. This average is 
ascertained by adding the amounts for the years 
selected and dividing the total thus obtained by 
the number of these years. The percentage in- 
crease or decrease is then computed for each of 
the years from this average amount. This is not 
advisable for the statistics in the chart on page 
124, as the number of years is only six. In those 
cases where it can be done there will likely be 
found a material difference between the move- 
ments of curves over a period of years thus dis- 
closed compared with the movements shown with 
only a single year as the base. 

The advantage of taking the average for a 
number of years as the base for computing in- 
creases or decreases is found in the fact that this 
average smooths out the irregularities of high and 
low or of large and small amounts which may have 
been comprised in the different years. If a 
single year only is used as the base it may be that 
in that particular year unusual influences or 



130 Chartography in Ten Lessons 

forces were at work to change unduly its total in 
comparison with preceding or following years 
and in consequence it is out of normal relation to 
the amounts of the other years. 

An illustration of this as to many phases of 
railway operation, for instance, is the fiscal year 
1908 extending from July 1, 1907, to June 30, 
1908, both inclusive. The records for that fiscal 
year include the effects ©f the panic in the latter 
part of the calendar year 1907. The railroads 
were very seriously affected by this disturbance 
in business and financial conditions and their 
traffic and revenue fell off strikingly. In con- 
sequence, any comparison of the operations and 
finances of subsequent years based upon the single 
year 1908 would show tendencies that might not 
and would not be shown if a year that did not 
record a panic was used as the base. Averaging 
a number of years escapes this possibility of 
statistical error and in consequence avoids 
misrepresentation in chartography. 

The proper lise of the average is an important 
asset to the chartographer. This average reper- 
sents or indicates the usual or common occurrence 
or status. It is, primarily, as has been stated, a 
problem of arithmetic. Quite often, if not always, 
it is simply an arithmetical standard, non-existent 
in actual reality and yet one around which other 



Value of Statistics to Ch autography 131 

facts tend to approximate or conform and by 
which they are measured or cbmpared. Such, 
for instance, as the average height of men, or 
the average price of a pound of bacon, and so on. 

THE MISUSE OF THE AVERAGE 

The average can be as much of a sinner when 
improperly made use of as it is a saint when 
properly employed. To the chartographer the 
use of the average has its pitfalls against which he 
must be constantly on his guard. While it is 
indispensable at times, it has its limitations and 
shortcomings and these must be known if he is 
to make the best use of it and not be inveigled 
by its attractions into grievous errors. 

Quite frequently the average comprises ele- 
ments radically different from each other whose 
irregularities or dissimilarities have disappeared 
or been smoothed out to such an extent that it 
does not represent any measurable status or even 
approximate situation of the actual facts, and in 
consequence can have no other effect than to mis- 
lead. This is illustrated, for instance, in statistics 
giving the average amount of stock held per 
stockholder in the railways of the United States. 

In 1914 this average was stated as $13,958. 
It was obtained by dividing the total number of 
stockholders — 622,284 — into the total par value 



132 Chartography in Ten Lessons 

capital stock outstanding— $8,685,764,000. Of 
course, such an average is absolutely meaningless. 
It is merely an arithmetic average. No such 
amount of stock approaches even in the slightest 
degree to the actual facts in the case. The 
fallacy in any practical use of this average can be 
demonstrated by a simple illustration from almost 
any railroad. 

Let us take the Wabash for an example. In 
1915 a single stockholder — the Equitable Trust 
Company — owned $28,744,000 of the stock of 
this railroad. With nine others, these ten largest 
stockholders together held $59,449,200 of the 
stock, or more than sixty -four per cent — nearly 
two- thirds. In view of these very large single 
holdings of stock by a very small number of 
stockholders — these ten owning by themselves 
an average of $5,944,920 — any arithmetical com- 
putation representing the average amount held 
by each stockholder cannot fairly represent the 
situation as to the ownership of stock in the 
Wabash Railroad Company. 

THE STATISTICAL CLASS LIMITS 

In such cases as this instead of making use of 
a meaningless average there is the possibility of 
recourse to a separation of a group of figures into 
class limits in order that the facts of a given situa- 



Value of Statistics to Chartography 133 

tion may be more accurately presented. This 
should always be taken advantage of whenever 
possible. 

Applied to the preceding illustration it simply 
means the separation of the total number of 
stockholders into groups or classes according to 
selected amounts of stock held. The first step 
in this statistical process is to determine upon 
the limitations for the different classes. These 
are purely arbitrary. To obtain them, round 
numbers are most desirable, as these give clear 
cut groups. These numerals form what are 
technically known as boundary lines of the classes. 

The difference between them is called statis- 
tically the class interval. These class intervals 
should all be equal or uniform. 

The number of classes and the number in 
each class become statistically what is called a 
frequency table. 

By thus dissecting the statistics a number of 
very interesting and highly important facts is 
usually disclosed which the presentation of the 
average does not indicate as being present. A 
knowledge of these facts is essential to a correct 
and complete presentation of the actual situation. 

These facts indicate that the chartographer 
must exercise his best judgment in the presen- 
tation of the average. He cannot be permitted 



134 Chartography in Ten Lessons 

to excuse himself by hiding behind statistics. 
Charts that reflect inaccuracies and irregulari- 
ties of mathematical computation to the extent 
of being misleading cannot be explained away 
because, in truth, they never should have been 
made. This is a high standard to attain, for 
quite often the chartographer must depend almost 
entirely upon his statistics for a truthful presen- 
tation of the facts, and if the statistics are faulty 
it seems rather unfair to hold the chartographer 
to strict responsibility for any misleading result. 
Nevertheless, the chartographer should be as 
scrupulous and as exacting in the use of statistics 
as in the use of the English language in maintain- 
ing a high standard for truthfulness and exactness. 

A sufficient variety of curve and bar charts 
have been presented in the preceding Lessons to 
impress upon the student of chartography that 
his most important task is the planning of the 
chart. It should be done before he touches pen 
to paper in beginning the drawing of the chart. 
With this planning successfully accomplished the 
remaining details of the work of execution or 
construction becomes a relatively simple matter. 

In this planning the student should first know 
thoroughly the real meaning or significance of 
the table of statistics he is to chart — he must 
"see" clearly the vital point of comparison the 



Value of Statistics to Chartography 135 

chart is to bring out. It is of advantage in com- 
prehending this point if the student will roughly 
sketch several different charts, both curve and 
bar, before he attempts to lay out the curve or 
bar in ink. He will be surprised at the difference 
in results shown by the various methods, and 
can then select the one which best illustrates the 
significance of the statistics. More time rela- 
tively should be given to the planning than to 
the actual drawing of the chart. The time 
devoted to the latter will be greatly shortened 
if the planning has been done correctly. Be- 
sides, it will also save time lost through changes 
and alterations usually made necessary where the 
planning has been neglected. 



QUESTIONS FOR SELF-EXAMINATION 

1. What is the value of statistics to chartography? 

2. What is the statistical table? How should it be 
arranged? 

3. Describe some of the technical aids to the interpreta- 
tion of a table of statistics. 

4. What are ratios? How are they computed? How 
arranged in table form? 

5. Describe the construction of a statistical table. 

6. What are the important differences between ratios 
and percentage increases or decreases? 

7. Of what value to the chartographer are percentage 
increases or decreases? 

8. Describe the zero line and its use in charts showing 
percentage increases or decreases. 

9. What is the average? How is it computed? Describe 
its advantages and disadvantages. 

10. What are statistical class limits? What are boun- 
dary lines of the classes? What is the class interval? A 
frequency table? 



1S6 



CARTOGRAPHY 

IN TEN LESSONS 

BYFRANKJ.WARNE 




LESSON X 

PRINCIPLES OF 
CHARTOGRAPHY 



Copyright. 1919, by F. J. Warne 
PUBLISHED BY 

FRANK J. WARNE 

SOUTHERN BUILDING 
WASHINGTON, D.C> 



e -n 



X. 



NOV -7 ibi9 



©CLA536473 



LESSON X 

Primary Principles of Chartography 

Planning the Chart — Importance of the Right 
Method — Essentials of Good Chart Making — 
Planning the Size of the Chart — Planning a 
Reduction in Size — The Reducing Glass — 
The French Curves — Checking up the Chart. 

Chart-making for commercial and other pur- 
poses is still in its infancy and in consequence 
has not yet been systematized. Statisticians who 
are employing it to an increasing extent as an 
aid in the presentation of facts are in disagree- 
ment, or rather are not in accord, as to the 
superiority of different methods. Give a group 
of statisticians who are also familiar with chartog- 
raphy a set of figures to chart and there will 
likely be as many different kinds of charts widely 
divergent in methods as there are statisticians. 
Thus the same information will be charted in 
many different ways. While variety in charting 
is possible where numerous illustrations must be 
made, at the same time some methods are better 
than others in bringing out the facts more clearly. 
Variety of effect is permissible and sometimes 
desirable in order to avoid monotony in presen- 
tation and to retain attention. 

137 



138 Chartography in Ten Lessons 

a choice of methods 

The value of the chart method being in ex- 
pressing clearly the meaning of a statistical table, 
the problem of the chartographer is to select the 
one method from among the many that will best 
express this meaning. Particularly is this true in 
the use of charts by the large corporation. Pre- 
pared usually for the executive whose time is 
limited and of great value, the chart must be so 
drawn as to give to him instantly the true sig- 
nificance of a mass of statistics which he has not 
the time to analyze in their details. The efficient 
and successful executive must decide quickly and 
of course correctly. The information furnished 
him on the chart must not only possess an ac- 
curate background but it must also be presented 
to the best advantage if he is to make the right 
decision and avoid "guess work." The busy 
executive is more and more being compelled to 
place greater dependence upon the chart analysis 
of statistics. 

As has been made clear, in the practice of 
chartography there is a choice of widely varying 
methods. No general rule can be given for 
determining which of these methods is the best 
for any particular purpose, but practice will 
enable one to form his own judgment as to selec- 
tion, and through experience he will learn to 



Primary Principles of Chartography 139 

choose the method best adapted to each of the 
varying problems. 

IMPORTANCE OF THE RIGHT METHOD 

The importance of selecting the best method is 
emphasized by Brinton in his Graphic Methods 
for Presenting Facts. He says: "After a person 
has collected data and studied a proposition with 
great care so that his own mind is made up as to 
the best solution for the problem, he is apt to 
feel that his work is about completed. Usually, 
however, when his own mind is made up, his 
task is only half done. The larger and more 
difficult part of the work is to convince the minds 
of others that the proposed solution is the best 
one — that all the recommendations are really 
necessary. Time after time it happens that 
some ignorant or presumptuous member of a 
committee or a board of directors will upset the 
carefully thought out plan of a man who knows 
the facts, simply because the man with the facts 
cannot present his facts readily enough to over- 
come the opposition. It is often with impotent 
exasperation that a person having the knowledge 
sees some fallacious conclusion accepted, or some 
wrong policy adopted, just because known facts 
cannot be marshalled and presented in such a 
manner as to be effective. 



140 Chartography in Ten Lessons 

"Millions of dollars yearly are spent in the 
collection of data, with the fond expectation 
that the data will automatically cause the correc- 
tion of the conditions studied. Though accurate 
data and real facts are valuable, when it comes to 
getting results the manner of presentation is 
ordinarily more important than the facts them- 
selves. The foundation of an edifice is of vast 
importance. Still, it is not the foundation but 
the structure built upon the foundation which 
gives the result for which the whole work was 
planned. As the cathedral is to its foundation so 
is an effective presentation of facts to the data." 

ESSENTIALS OF GOOD CHART-MAKING 

The primary essentials of good chart-making 
are simplicity and clearness. The curves or bars 
of a chart are employed to express and to com- 
municate ideas, just as words are used in the 
English language. The fewer the ideas it is 
attempted to express in a single chart, the better. 
In fact, a single chart should aim to express only 
a single idea. This is difficult to accomplish, 
as the essence of a chart is a relation or a compari- 
son and this usually involves more than one idea. 
The aim, however, should be to construct the 
chart so that all but the dominant idea it is 
intended to express or communicate is kept 



Primary Principles of Chartography 141 

subordinate or in the background. There should 
not be a single unnecessary mark or figure or 
word on the completed chart, and if its full 
meaning cannot be grasped quickly, then it has 
failed of its object. 

There is a common and quite general violation 
of these principles. Chart-making is not at all 
complex; it does not involve a knowledge of 
higher mathematics for correct presentation and 
interpretation. There are a few definite rules 
which, if once understood, result in the ease and 
facility that may be likened to a knowledge of 
the alphabet, once acquired. Much of bad chart- 
making and of confusion in interpretation flows 
from a violation of the few simple principles. 

PLANNING THE SIZE OF THE CHART 

One task that will likely confront the student 
with as many perplexities as any other will be 
the working out of the size of the chart within 
the limitations of the sheet and the requirements 
of the statistics. Only practice will enable him in 
time to overcome most of these difficulties. But 
as a sort of guide for meeting some of these prob- 
lems there is presented in the following paragraph 
a practical illustration. 

The size of the sheet for the completed chart is 
arbitrarily fixed for us at 12 by 16 inches. At 



142 Chartography in Ten Lessons 

least two of the 16 inches are required as a margin 
on the left of the sheet (the chart appearing 
lengthwise) for binding. Usually an inch margin 
on the remaining three edges is advisable. This 
leaves 13 of the original 16 and 10 of the original 
12 inches as the size within which the chartog- 
rapher is to work, or a size 10 by 13 inches. The 
neat lines of the frame and the letters of the title 
must come within this size. Usually one-half inch 
is sufficient for the title letters, and in our particu- 
lar illustration it is required that the title appear 
lengthwise of the sheet. This reduces the size to 
9.5 by 13 inches. Between each of the neat lines 
and each of the scale -lines one-half inch will 
usually be sufficient — this is a reduction in both 
dimensions of another inch. Sometimes a full 
inch is required below the lower horizontal line 
for the footnotes. Of course these spacings are 
subject to being increased or decreased according 
to the requirements of varying problems. The 
original size of 12 by 16 inches has dwindled by the 
above mentioned processes to 8.5 by 12 inches as 
the size of the framework proper. 

The arbitrary limitations of space within which 
the chartographer is confined in his work cannot 
be removed from among the difficulties of the 
practice of the art. All that he can do is to learn 
by experience to make the best adjustment pos- 



Primary Principles of Chartography 143 

sible in each particular problem. This is true 
no matter what the size is that is determined upon. 
And having made the decision the chartographer 
will soon learn to adapt himself to the limitations 
of space and to forego something that is desirable 
in order to adjust his work to the exigencies of the 
requirements. 

In most cases where a number and variety of 
charts are to be filed for reference or bound as 
exhibits it is quite important that the size for all 
the sheets be made uniform. This does not neces- 
sarily mean that the worker will have the same 
size for the original of all the charts themselves, 
but it does mean that the completed charts shall 
all be on sheets of the same size. This permits of 
uniformity in size for all completed charts and 
assists in securing neatness and orderliness in 
office records. Completed charts on sheets of 
different sizes are awkward in handling and easily 
damaged. 

PLANNING A REDUCTION IN SIZE 

Where the original drawing is to be reproduced 
by one of the several photographic processes and 
printed from plates, the chartographer has a 
special problem of reduction in size to solve. In 
such cases the pen-and-ink chart should always be 
considerably larger than the final reproduction. 
Most charts will stand a reduction in size of from 



144 Chartography in Ten Lessons 

one-third to one-half and in cases even more, and 
will be improved in appearance by the process. 
A reduction in the size of the original drawing 
tends to smooth out the rough places or minor 
irregularities of lines, curves, bars, figures, and 
letters and results in a much cleaner effect. 
Virtually all the charts in these lessons have been 
reduced approximately one-half from the size of 
their original drawings. 

In ascertaining the dimensions for the size 
of the original drawing simply apply the rules of 
proportion. Only four factors are involved — 
the width and length of the reproduced chart 
and the width and length of the size that 
must be drawn to secure the reproduced size. 
Assuming our problem to be the one mentioned 
on page 142, we know the width and length of 
the reproduced size — the former is 10 inches and 
the latter 13 inches. We know also how much of a 
reduction we desire to secure — whether one- 
third or one-half and so on. Selecting a reduction 
of one-third gives us the arbitrary width of the 
original as 15 inches. It is the length of the 
original that must next be learned. 

Our known figures give us this formula: 
10 : 13 : : 15 : x, which reads 10 is to 13 as is 15 to x. 
Working out this formula we learn that 13 times 
15 equals 195 and this number divided by 10 gives 



Primary Principles of Chartography 145 

19.5. This latter thus represents our unknown 
fourth quantity, which is the dimension of the 
length of the original drawing. The size of the 
original must then be 15 by 19.5 inches to secure a 
reduced size of 10 by 13 inches. 

In the above illustration the number 10 and the 
letter x are known as extremes and the numbers 13 
and 15 as means. In any proportion the product 
of the extremes is equal to the product of the 
means, that is, 10 times x, the latter being 19.5, 
is 195, the product of the extremes, and 13 times 
15 is 195, the product of the means. 

It is also true that the product of the extremes 
divided by either mean gives the other mean, as 
for instance: The product of the extremes is 195 
(10 times 19.5) and 195 divided by 13, one of 
the means, gives 15, the other mean, or 195 divided 
by 15 gives 13. Again, the product of the means 
divided by either extreme gives the other extreme. 
For illustration: 13 times 15 is 195, the product of 
the means, and divided by 10 gives 19.5, or by 
19.5 gives 10. 

Another simple method for ascertaining the 
reduced dimensions from the original is illustrated 
on the following page. The larger rectangle is 
our original size. From its lower left hand corner 
a diagonal line is drawn in light lead pencil to the 
upper right-hand corner. This is line C-C. This 



Primary Principles of Chartography 147 

diagonal line is then connected by a vertical line 
starting at any point on the base line A-A, such as 
the broken line shown. From the junction point of 
the broken line and the diagonal line draw another 
broken line at right angles to the vertical line and 
extending to line D-D. The rectangle thus cir- 
cumscribed in the lower left hand corner will be 
found to be in exact proportion to the larger rec- 
tangle, or the size of the original. 

In planning a reduction in the size of the 
chart from the original, care should be exercised 
in seeing that all the lines on the original are made 
sufficiently wide to stand the reduction in line 
width due to the decrease in size. In our preced- 
ing illustration on page 144 the lines would be only 
one-third as wide in the completed as in the 
original drawing. Therefore, all the lines and 
curves and so on of the original must be made 
wider than would be necessary if the chart were 
not to be reduced. Failure to allow for this reduc- 
tion in the width of the lines and curves and let- 
ters and figures is a common mistake made by the 
beginner in chartography which should be 
guarded against if the best results are to be 
secured. 

THE REDUCING GLASS 

A valuable aid in this branch of the work is the 
reducing glass. It may be said to be the opposite 



148 Chartography in Ten Lessons 

of the magnifying glass, decreasing instead of 
increasing the size of the object observed, the 
lens being ground concave instead of convex. 
A convenient size is one with a single lens about 
one and three-fourths inches in diameter. This 
permits the lines, figures, and letters on a chart 
to be seen in sizes from one-half to one-fourth 
smaller than their originals. 

In observing the parts of the chart for an in- 
dication of the size of the proposed reduction the 
most accurate method is to hold the glass at 
different distances above the sheet so that looking 
through it with the left eye two or three or four 
squares, depending upon the amount of reduction 
desired, equals one square as seen by the unob- 
structed right eye. Thus by superimposing and 
comparing the images of both eyes the required 
reduction can be measured. This enables a 
comparison of the width of lines, figures, and 
letters as originally placed with their width after 
reduction and permits the determination as to 
whether they must be made still wider or heavier 
or larger in order to meet the reduced size. 
Even with the use of the reducing glass the be- 
ginner is likely to find at first that his lines, 
curves, figures, letters, and so on when reproduced 
do not appear to be as heavy or as large as he had 
anticipated. 



Primary Principles of Chartography 149 

Without the employment of these rules and 
aids in reduction one has to depend largely upon 
guess work as to whether the chart and its parts 
will present a proper appearance when reduced, 
and guess work, as has been said, should be 
eliminated from chartography. The student 
must not forget that accuracy is a valuable 
mental quality which is useful elsewhere than in 
chartography, and if the practice of this art 
teaches it to him he has gained an additional 
asset of great usefulness. 

THE FRENCH CURVES 

Another tool that the student may find useful, 
especially in charting curves, is what is known as 
the " French curves." These are on sale at any 
first-class store dealing in drafting instruments. 
While they do not always in their entirety fit into 
the complete curve the student has to make, they 
can be shifted forward or backward so as to cover 
fairly accurately the lead-pencil dots measuring 
the points of contact of the curve. Usually 
they give a clean, smooth curve if care is exercised 
in their use. 

In most charts where the scale units permit the 
curve to move regularly up or down across the 
sheet, the curve appears smooth without sharp 
movements that result in peaks. In all the 



150 Chartography in Ten Lessons 

illustrations in these Lessons these curves have 
been drawn in freehand, and this method is 
recommended as satisfactory. This peak-top 
does not indicate as minute a degree of accuracy 
in the figures upon which the curve is based as 
does the smooth curve. 

OTHER MECHANICAL AIDS 

One serious drawback in making the letters by 
hand is the length of time required, even after one 
becomes proficient in lettering. Under conditions 
where the number of charts to be drawn is large, 
efficiency is best served and the cost of produc- 
tion materially reduced if recourse is had to a 
small printing press with about three fonts of 
type of 18, 12, and 10 point, commercial Gothic. 
The moderate expenditure will soon be com- 
pensated by using for other work the time saved 
from lettering by hand. Printed letters photo- 
graph satisfactorily in almost any process of 
reproduction. 

Another recourse instead of drawing letters by 
hand is to make use of gummed black paper 
letters and figures which are for sale at first- 
class stationery stores. These can J usually be 
pasted quite neatly on the chart that is to be 
reproduced, if a light pencil line is made for a 
guide along the bottom of the|spacing for the 



Primary Principles of Chartography 151 

letters. This pencil line must of course afterwards 
be erased. 

CHECKING-UP THE COMPLETED CHART 

After the drawing has been finished there 
remains for the student a very important task. 
The explanation of this task in detail involves 
describing the concrete application of all the 
rules and principles of chartography that have 
been observed in the construction of the chart. 
This is true in the sense that the student must see 
to it, by a rigid and thorough checking-up of the 
lines and figures and letters and so on before the 
chart leaves his hands, that all these rules have 
been strictly applied. As related to the check- 
ing up of certain features of the curve chart, 
this task has already been referred to in Lesson 
IV, pages 50 and 51. The immediately follow- 
ing statements apply particularly to the bar chart. 

Each bar should extend to the point on the 
chart that its statistical number as measured by 
the scale determines — it should neither fall short 
of this point nor extend beyond it. 

Be sure that each bar is properly spaced from 
adjoining bars. 

In making the bars of a chart it is quite often 
possible that all the space to the right of the 
vertical scale or column of years and to the left of 



152 Chartography in Ten Lessons 

the ends of the bars, and from the horizontal 
scale line to the base line, can be made black 
with a small brush dipped in India ink, the ends 
of the bars being squared with the pen. After 
the ink dries the bars can easily be outlined and 
separated from each other according to the ver- 
tical scale units by drawing horizontal lines in 
Chinese white. This expedient enables a great 
deal of work to be done in a comparatively short 
space of time, and the results are highly satis- 
factory. When the India ink is used in this way 
it is advisable to apply two or more coats or 
washes in order to insure a uniform density of 
surface. 

Chinese white is an opaque composition which 
may be thinned down to desired consistency by the 
addition of water. Besides its use in separating 
bars out of a block of black, Chinese white is also 
excellent for concealing black ink lines or marks 
where erasure is impracticable. 

The scale units should be correct at each of the 
points of measurement and neither to the right nor 
left of their proper places. 

The chart should include the statistical table 
from which it has been made. 

If it is found impossible to include the statistical 
table on the chart it should be on an accompany- 
ing or attached slip or sheet. 



Primary Principles of Chartography 153 

The table of figures should be correct and neat 
and properly located and boxed without crowding. 

The period of time column both in the table 
and adjacent to the bars must be correctly and 
properly alligned. 

Be sure that no mistake has been made in copy- 
ing any figures on to the chart. 

The statistical table involving periods of time 
should be presented with the earliest period first. 

The source of the statistical table should in 
every instance be given, preferably in the foot- 
notes. 

Instead of checking up the movement of the 
bars or curves from either the statistical table on 
the chart or the scale figures themselves, reference 
should be had to the original figures. 

All additions, subtractions, multiplications, 
divisions, and so on derived from the statistical 
table should be computed at least twice and by 
different persons. 

See that all horizontal lettering reads from left 
to right and all vertical lettering from the base 
of the chart upward. 

The title should be clear and concise and yet 
comprehensive. It should have every word 
spelled correctly and should contain the fewest 
possible words consistent with clearness of ex- 
pression. It sometimes happens that the title 



154 Chartography in Ten Lessons 

can be improved in these directions over the first 
selection of words after the student has been 
working with the statistical material. Words as 
well as letters in the title should be evenly placed 
and spaced — none of them must be askew. 

THE PROCEDURE IN CHECKING UP 

It is an advantage in checking up a chart to 
start with the title, next the horizontal scale, then 
the vertical scale, the table of statistics, and then 
relate the movement of the curves or bars to 
these factors. The horizontal and vertical lines 
forming the background of the chart must not be 
overlooked as to their proper distance apart. 
The foot-notes and the neat lines require equally 
careful attention. 

Make sure that the neat lines are wider or 
heavier than the vertical and horizontal lines of 
the framework. 

Foot-notes should be as brief as possible con- 
sistent with clearness, should read from left to 
right, and should not be askew. 

In selecting the designations for the curves and 
bars, have the most conspicuous been made to 
correspond with the particular statistical element 
it is desired to emphasize? For instance, in bar 
designations the solid black is generally more 
noticeable. 



Pkimary Principles of Chartography 155 

Check carefully the key or legend designations 
with those of the curves and bars to see that 
they correspond accurately. 

Have the proportions been correctly determined 
for the required reduction? 

Be especially careful that all lead pencil and 
unnecessary ink marks, used as guides or other- 
wise, have been erased or removed. If not, in 
case of reproduction these are likely to photograph 
and thus affect disadvantageously the neat ap- 
pearance of the chart. 

CLEANLINESS ESSENTIAL TO NEATNESS 

In handling a chart keep the hands clean, 
especially from the drawing ink which will smear 
the sheet. An aid to this will be found by keeping 
the ink bottle on a blotter which will absorb drops 
and prevent them from getting on the drawing 
board or table. Blot immediately every ink spot. 

Never fold a chart. Keep the sheet flat or 
roll it. A folded chart cracks or creases the sheet 
and breaks the lines, bars, curves, and so on. 

All checking and verification should be done 
also by some one other than the person who drew 
the chart so that there may be greater certainty in 
the detection and correction of errors. For 
even the best chartographer makes mistakes. 

The student should assure himself before per- 



156 Chartography in Ten Lessons 

mitting the chart to leave his hands as completed 
that in all respects it is in condition to receive his 
final O. K. 

PLOTTING THE CHART IN ROUGH OUTLINE 

After the chartographer has completed his 
checking up he should devote several minutes to a 
consideration of the possibility that he might 
have selected a different method which would 
have brought out the point of the statistics more 
clearly. He will have fewer regrets if he adopts 
and consistently follows the practice of first 
plotting his chart in rough outline in lead pencil 
at the very outset of his work. He should apply 
this to several methods before finally determining 
upon any. He will find that though this practice 
takes a little time at first it will in the end greatly 
expedite his work. 

It should never be forgotten that as chartog- 
raphy primarily supplements statistics with the 
object of making them clear and comprehensible 
at a glance, a chart that is not more clear in 
exposition than the statistical data upon which 
it is based has missed its object. Also it should 
be remembered that the chart " tells the story " — 
it should need very little explanation, if any. 

Instructions to the lithographer should be clear 
and definite. These may be written on a slip of 



Primary Principles of Chartography 157 

paper and attached to the drawing with a clip, 
but a safer plan is to write them on the coordinate 
sheet itself, preferably on the back. 

Before sending the drawing to be reproduced 
be sure to cut away the margin of the sheet where 
the thumb tacks have held it in place on the 
drawing board, as these punctures are likely to 
show in the reproduced chart. Even when the 
drawing is not to be photographed, such punc- 
tures in the paper detract from the neat ap- 
pearance of the finished chart. 

Before deciding upon the uniform size of sheet 
for a number of different kinds of charts it is 
advisable to consult the lithographer in order that 
a size may be selected which permits of the least 
possible waste or loss in cutting from the larger sheet. 

It is important also to examine closely into 
the quality of the paper of the reproduced chart. 
The preservation of the chart depends to a large 
degree upon this quality. Paper containing 
sulphite pulp or other chemicals suffers rapid 
deterioration. Within a short time such paper 
becomes brittle and discolored, and these defects 
seriously affect the preservation of chart records 
for any length of time. A high grade linen bond 
paper, although it costs more per sheet, is less 
expensive in the long run. 

The checking up of the completed chart as well 



158 Chartography in Ten Lessons 

as the details of the planning and drawing should 
impress upon the student the necessity for observ- 
ing closely and carefully every factor with which 
he deals. He cannot afford to overlook even 
the smallest detail as every detail must be accurate 
if the completed chart is to be accurate. This 
attention to minor details fixes the mind upon 
the correctness of the figures; on the accuracy 
of the scale units; on the spacing of figures and 
lines; on the spelling of words; on the correct 
designation and spacing and length of the bars, 
and so on. Looking for possible defects or 
errors develops the critical faculties. In the 
course of practice all these separate but important 
details soon fix a habit of mind and that which at 
first may be hard work sooner or later becomes 
almost mechanical attention. Working with 
tools that require accuracy in their use the 
chartographer soon learns from mistakes he must 
correct that it does not pay to make mistakes — 
that it is a loss of time and energy and materials 
— and he comes consciously to apply himself so 
as to avoid their repetition in order not to be 
compelled to do the work over again. Out of this 
experience he learns efficiency in the concen- 
tration of his energies and in their application to 
his specific task. Chartography is thus an 
invaluable mental training. It lends accuracy to 



Primary Principles of Chartography 159 

constructive thinking; it leads to the further study 
of statistics and of the underlying forces back of 
them, and by these and similar steps the pro- 
gressive student develops his thinking capabilities. 

QUESTIONS FOR SELF-EXAMINATION 

1. What is meant by planning the chart? How does it 
differ from plotting the chart? 

2. Discuss the importance of selecting the right method. 

3. What are the essentials of good chartography? 

4. How is the size of the chart planned? 

5. How is a reduction in size of the original determined? 

6. Of what assistance is the reducing glass? 

7. What are "French curves"? 

8. Describe the more important phases of checking up 
the completed chart. 

9. Summarize briefly the more important of the funda- 
mental principles of chartography. 

10. Of what value is chartography in training the mind? 



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